Cold start fast idle problem 1.8i - problem with system?

I posted this today under Fuel and Exhaust but the system doesn't seem to be sending the confirmation out. Am trying here to see if it works now. Hope you don't mind.

Hi All,
After 5000 miles of driving my Golf Mk1 with 129k miles is starting to give some problems. The facts:
- There is a coolant leak, I think from around the level sensor on the header tank. I keep topping it up at the moment till I get time to fix it.
- Cold & warm starts fine.
- Cold start make the idle go up to say 1250.
- Drive away and drive for 1/2 hour and the idle will be up to 2000+
- A couple of kicks on the throttle drops the idle but it comes up again at the next traffic lights. The car is definitely warm.
- turning off & then again on (the engine) fixes the problem when the car is warm.
It sounds like a sensor to me but I don't know where to look or start. Help much appreciated.

Thanks
Arn

1991 Sportline LHD

I believe this could be the warm up regulator.if you search for this you should get plenty of info.
hope that helps