My 1996 XJR has developed an interesting problem: once the engine is warm and the car has been parked up with the engine off for, say, 20-30 minutes, when I turn on the ignition again the temperature gauge shows higher than "normal", despite not having climbed above normal beforehand.

Any ideas?

When the ignition's on the fans run constantly but VERY rarely remain on after the ignition has been turned off.

 

That's perfectly normal. All liquid cooled engine do this, it's call heat soakback. Once the engine is shutoff, the coolant ceases to circulate. The residual heat from the engine itself raises the temperature of the trapped coolant giving the unusual gauge indication.