Overheat Warning Issue

[mattp]

Hi guys, thought I'd see if anyone has had this issue before...
It started a few months back, I turned the car on, the thermostat on the dash beeped frantically and the needle went up into the red saying I was overheating, so I immediately turned the car off, sat there for a few minutes with the bonnet up, then tried again and it was all good. This happened a couple of times, but somehow I noticed that if I didn't turn the car off straight away it would stop beeping and drop rapidly back down to where it should be at the bottom end of NORMAL (like in the matter of 5 seconds). It's started doing it maybe once a week I guess, in the last couple of weeks, and since I'm not actually overheating (like it happens when the cars been parked all day, I get in and turn it on and it does it, before dropping back down). Would it be a thermostat issue, or what are the thoughts of others? I'm hoping it won't be too expensive, but I can't see it being major (fingers crossed!), since the car runs like a dream so seems more like it'd be a sensor or something. Any advice is much appreciated, cheers, Matt.