Hot!Engine not turning over intermittently

Having read the above I would suspect the likely suspect may be at the starter motor, and perhaps more than likely the solenoid. The clicking you hear could perhaps be either the relay that controls the solenoid or the solenoid it`s self..? 
That you have replaced the earth leads and hopefully cleaned both ends where they connect to the engine chassis/gearbox or whatever to ensure good contact... and that the connections at the solenoid are not corroded or loose...  A test perhaps worth trying to determine whether the issue might be battery or starter related, is to switch on the headlights, and try to start the engine.... If all you get is the click you mention, and the lights dim considerably then chances are that it is battery related. 
If all you get is slight or no headlight dimming and hear the click when you turn the key to engage the starter, then the issue would seem to be starter related.
If starter related then the solenoid is perhaps favourite, The solenoid is just a heavy duty relay.  
When you turn the ign key to engage the start sequence,  that switching action then provides power to the coil of the first relay in the circuit, which will logically emit a click as it`s contacts close, those contacts when closed  then pass on power to switch on the coil within the second relay in the form of the solenoid mounted on the side of the starter motor,  it creates a louder click, with the coil in the solenoid now energised causing the starter motor`s gearwheel to engage the flywheel with a clunk, and once engaged the heavy duty contacts in the solenoid then close to make the starter motor live and turn the engine over  
Thus a small relay switches on a larger relay which then switches on the starter motor..
The contacts in the solenoid can burn over time given the high degree of power that they are dealing with it is normal for them to fail intermittently over some time prior to total failure..  My thinking behind having the headlights on is to determine whether the contacts in the solenoid are passing current/power to the starter motor it`s self. In the case where the contacts have failed/burned and are passing no power and all you hear is the click you describe, the headlights are unlikely to dim to any great degree, as the load of the starter has not been switched through to the battery..
New solenoids can be bought independently of the starter, though if the starter has seen a lot of service it might be best to bight the bullet and buy a new or reconditioned unit..?
I have stripped and repaired a solenoid with burned contacts on a friends 928.. simple if you know how, though given the cost of buying a new solenoid, hardly worth the bother..
Hope this helps in some way.
Feel free to suggest where I might be mistaken,

I suspect that there are few who would take the time to "service" a solenoid on the basis of any reasonable cost benifit analysis, given the relativly low cost of a solenoid.   
 
As for "reconditioned" there would seem to be a whole world of difference in terms of quality/rip off out there in the recon marketplace..?
 
The only reason I stripped and "repaired" the 928 starter was that my friend was visiting and needed the car to get home with no chance of finding a replacement solenoid on the day..!

 
Thanks i tried starting car with the lights on and they go out completely when it doesnt turn over.  After waiting 30 seconds or so i turn on the ignition again and lights go out completely again however this time engine turns over and car starts.  Looks like it is the battery then so I’ll look at replacing battery as a next step.  
 
 
 
 
 

Personally, I would go to my local tyre and battery service dealer and ask him to check the discharge rate and at the same time the charging rate, just to confirm. I have had this type of issue on other vehicles. Sometimes the alternator is not putting enough back into the battery or the battery will not hold its charge due to the high demand on start up.
 

MarkGolf
Only just read this, I had a similar thing, car on a CTEK for extended period, car would just clunk.. then after some tried, get lucky and fire. 
 
I noticed I would never have this problem after a run or days after. It was just being sat for a long period that I would get this. I performed all sorts of tests and found that the battery would just be under 12v on occasion and this would result in the non start. If I put jump leads on with another car connected, fired up instantly. Battery performed fine in all tests by a garage. 
 
It would be interesting, that when your car does this, if you join another car/jump leads, does it fire instantly or not. 
 
During all of this, I had changed the voltage reg on my alternator also as I heard these can cause issues with drain. I still got the issue once after changing this so I'm not sure it did anything for me but I definitely noticed the car didn't respond well to long periods of not being used even with the CTEK.. All my earths were renewed/cleaned, starter solenoid inspected etc.
 
My next option was a battery with more CCA.

Spot on, I would always go for the largest capacity Cold Cranking for my vehicles. I do a lot of short runs, therefore I have all my vehicles connected to battery conditioners. Starting up an engine takes so much power from your battery and short runs, especially in winter with heaters running etc.

...perhaps a wee bit clutching at straws, but how old is the battery tender?
 
Reason I ask is that when my car was not starting I was going through much of what you are trying to fix it.  I've used an Optimate111 and when I contacted them to see if there was a check I could do Optimate advised that, due to it's age (bought in 2000!) it may well be past its best and suggested an Optimate5 would probably be better suited as it has a greater output.  Don't know if that was just a salesman talking or genuine advice.  I didn't find out how to check it either, mind, but now use a Lidl unit bought as back-up when they were on offer.
 
All that said, of course, I had the starter changed and all now seems well.
 
Because all the lights work it doesn't necessarily mean the tender is operating at its best.

geedee
Nothing wrong with clutching at straws Les.
Chargers come in a variety of types, the ideal for seldom used cars would seem to be the float/conditioner type of chargers that sense the battery voltage  and adjust the charge accordingly to bring it up to the ideal voltage.
As for the TIME it might take to get up to full voltage that is dependant on a few factors though primarily the maximum charger output.
The age/condition of the battery is key in terms of it`s ability to retain charge over TIME, A battery may read well on a voltmeter but as soon as a load is put upon it, the voltage can drop off considerably, and no more so than when trying to crank the engine over. 
I have two CTEK chargers, one for ordinary old style wet lead acid batteries,  and the other a newer version which can charge and condition either ordinary wet lead acid batteries, or the newer type Advanced Glass Mat batteries as will be found in vehicles with stop/start operation...
As best I understand it the AGM batteries if fitted to an air cooled or similar age machine, will never get up to full charge as the AGM max is a higher voltage than the older led acid type, thus the alternator`s inbuilt voltage regulator will have a max voltage setting lower than the AGM type battery`s max voltage.. Similarly old style float chargers may also not bring an AGM battery up to a fully charged state..?

I was surprised at the time it took my battery to reach full charge with my Ctek charger. My first thoughts were the charger was goosed, but no it eventually got there. AGM batteries as far as I am aware are for use with the stop/start functionality.

Thanks for taking the time to reply Stephen, crud between the battery terminals and the vehicles clamps is a bit of a rarity. It is possible that even a new CTEK can find it`s self in a situation where it may not keep up with a parasitic drain.. I suspect your CTEK`s max output is circa 5 amps, thus a drain anywhere near that cause the CTEK to be running HOT in time as the result of trying to keep up with the battery discharge rate, as opposed to the charger eventually running at lower current levels expected as the battery comes up to a fully charged state..?
OK so unlikely to have a parasitic loss that high ( I hope) but alarm and other location/anti theft devices have been known to cause issues that can be intermittent and draw current when the car is left to it`s own devices for lengthy periods (ie not a daily) that combined with an older battery that may have been living a difficult life of irregular charging, possibly been allowed to run flat on occasion and when next charged used to crank a reluctant machine to fire up... all of which can prematurely age a battery and reduce it`s capacity to hold charge.
Any and all the aforementioned can add together to create the issues you seem to be suffering and if you add to that a reluctant starter motor...?
Looking forward to reading you have it resolved SOON..
EDIT :-  Forgot to mention for anyone else reading this with similar issues...  parasitic losses causing the battery to discharge over TIME and due to lack of regular use can be overcome by fitting a battery isolator switch, though much depends upon any circuit which may be a bother to reprogramme as the result of isolating the battery and reconnection..?  

 "With new battery car starts first time from cold both times I've tried so it does look like issue was with the battery."
 
For sure things can appear that way, only time will tell, so keeping my fingers crossed for you.  I have zero experience with the CTEK monitor but being blue tooth I imagine it will draw a few ma to operate, thus adding to whatever losses the battery experiences over time..?