Warm starting problem Arnage

[Jinto100]

Hi, I have a 2002 Arnage T with about 40k on the clock. I think this problem has existed since I have had the car (about a year) and only seems to occur when the engine is warm, not hot, so perhaps if I have left it for 40 minutes or so after a run. When I start the car it does start fist time, but cranks longer than when cold, and when it fires it runs very rough for about a minute, like it's only running on half the pots. During this time the accelerator seems to be inactive and only once the idle smooths out does the accelerator seem to have any effect. It starts fine when cold and when hot. I'm thinking it may be a coolant sensor, in which case it could potentially be an easy fix myself, or perhaps something more complex. Has anyone else has a similar issue?

Many thanks!
Mark