High idle issue

The m.o.t is due and we have a problem. 
Problem is that the car starts and runs fine but after the initial warm up the revs seem to hang at 1k and the radiator fan cuts in really early. 
I have had a search around and it seems to point to a problem with the coolant temperature sensor. 
Is this the most likely cause or could it be a stuck thermostat?

Might you have air getting in to the inlet manifold?
M

Also, have you tried resetting the stepper motor?

Does the car have a plastic throttle body? Probably not but just a thought.

It might be useful for some members if you were to cover the reasoning behind your comment. It doesn’t crop up anywhere near as much these days but there will be early cars with early TBs whose owner might be scratching their heads over this ancient & irritating problem
M

Ah yes the bloody awful plastic throttle body, no doubt another brilliant idea of the bean counters.
My car still had one when I bought it, and true to form the damned thing was distorted as they all end up being, and the butter fly doesn't close properly giving an annoyingly high idle.
The cure is fit a alloy one, better still fit the larger sized 52mm unit, it won't really give you anymore power than the 48mm unit but it shows in better drivability, the car seems punchier.
Don't bother going to the 55mm throttle body, it's too big and doesn't work as well.....I ventured down that road so you don't have to!
Having said that I'd be surprised if there are any cars left still running, around sporting the plastic 48mm throttle body. Surely the damned things should all have been replaced with alloy ones by now.
 

Thanks everyone. 
I  think that I got too focused on the fact that the radiator fan kicked in early and saw some posts with the same symptoms. 
I will go back to basics and start with resetting the sensor then change this...
Hopefully this will resolve the problem. 

By gum that is an historic object! Am I seeing an original plastic SU throttle body or are my rheumy old eyes playing tricks?
You might have become the last person to be plagued with this.
Bung a 52mm TB on, you won’t, as Cobb’s says find it faster, more urgent is probably a better description.
M

It seems that my question and thought were bang on with regard to a plastic throttle body.
As we know its a sticky situation.

That throttle body is a museum piece!