Ford Probe stuttering probe (engine coolant temperature sensor problem, maybe?)

Wondered if someone could advise regarding the issues that I'm having with my 1996 Ford Probe? I've owned the car since 1999 and for the last few years I've been having a problem that seems to be getting progressively worse - especially during the winter time. Also because I live in London now and don't use my car as much as I used to (about once a week) it's very noticeable.

The car starts first time and runs ok for about 10 minutes or so, but after those 10 minutes it becomes really sluggish when changing gears. It's like there's no power coming from the engine, or almost as if the fuel can't get into the engine. When I pull off in first or change from first to second I really have to keep the revs high otherwise it will stall.

On really cold days (and if I haven't used the car for maybe a week or so) it is especially terrible. However, after about 30 minutes the car is perfectly fine and a real pleasure to drive. It's just that bit in between which is causing the biggest issue for me.

I'm starting to wonder if it could be a faulty Engine Coolant Temperature Sensor? The sensor is telling engine is hot enough when it isn't...

Any advice would be greatly appreciated!

Cheers!