Good morning, I am new here, having recently purchased my first K100RT.

Whilst out riding a few days ago, the engine lost power, it was probably only running on two cylinders. It was 25C a warm day (for the UK), I had ridden about 20 miles on country roads and there were no indications or warnings before the stoppage.
I checked that the plug caps were secure, the relays were properly seated and the fuses were all OK. I also opened the fuel cap in case there might be a vapour lock and checked that the fuel pump was running. I did notice that the crank case breather was split. The engine would start but refused to rev or tick over.
After an hour or so I called the recovery service and eventually arrived home about 4 hours after the initial break down. After getting the motorcycle of the trailer, I pressed the starter the engine fired and ran perfectly, I was able to ride it normally
It seems clear to me that the problem is related to temperature although the engine temperature warning light was not illuminated or the fan running at the time of the stoppage. I have previously tested both the warning light and fan to ensure they are operational.
Is there anyone out there that might have any ideas or suggestions of what to check or what the problem might be.

Sounds like Hall Effect Sensor, 
As a test - start the engine when it is cold and direct a hairdryer at the T shaped cover on the front of the engine, if the engine cuts out that is your problem. Use the search function - lots of info here on that issue

Morning Romille   First thing put the VIN No in so the brains can be precise with their info, My first thoughts are Hall Effect Sensor Unit faulty. I have a spare one should you wish  to borrow, rather than buy one and waste money.Im in Brighouse feel free to PM ME and we can do what we can to solve the issue

It's also possible it's a faulty coil.

If you can gauge the cylinders that stop firing, either 1/4 or 2/3. Being careful you can check the temperature of the headers.

Front coil is for 1/4 and rear for 2/3. Failing Hall Sensor or failing coil affects them in this configuration. Exchange the coils, they are identical apart from the labels, see if the faulty cylinders change over. If yes, then its a coil problem, if not then its Hall Sensor problem. Early coils are very prone to failure after they heat up.

Welcome to the club! There are couple of others here in the same fix right now. Have you checked the fuel lines in the tank to be certain they are fastened? Have you checked them for obstructions? Have you replaced the fuel filter yet?

Let me add my vote for Hall Sensors or coils.  Based on your account my money is on the Hall Sensors. 

Early coils had a weakness in the potting that allowed spark leak while the Hall Sensors have a tendency to totally fail gradually and usually fail when hot and start working again when they cool off.

Even if you find that the coils is not the problem, I would suggest that you begin a search for a pair of good used late model coils to replace the ones on the bike.  Sooner or later, your coils will fail and the later coils, while still available, are getting pretty expensive.