1997 Jaguar XJ6 wont start when hot

First thing you need to do is have the codes read, Autozone does it free, Post the results with the code number(s). Even if the service engine light is not on, there should be freeze frame data stored.
If it won't make it to Autozone, buy a cheap scanner, they can be had for 30-40 dollars, a good investment, since they cover all cars sold in the USA from 96 on. Tho I am not a Jag guy, it could be a problem with the engine coolant temp sensor, or the crank sensor.