C3 pluriel overheating but isn't!

Hi I'm new and wondering if anyone has any ideas on my Citroen c3 pluriel overheating problem.

It's says it's overheating when its actually not. Hood and underneath it not hot. Every so often it will been 3 times and say it's overheating. I pull over check and it's not and once the fan has cycled off it's back to one bar. And issue won't happen again for a while then drive say a longer journey it will happen again only on longer journeys. Engine management light was on first time it happen said temp sensor so we changed this. (Old one got snapped off whole trying to indo by partner and had to be still out at garage). I'm not generally worried about it but have no idea what else it can be (I'm a woman after all) the electrics are crap in other areas which if seen is a common problem. Anyone have any thoughts?? Also engine management light is on for cat bit had it looked at and it's apparently fine.

I'm also not keen to throw loads of money at car as it's been written off by insurance as a cat n as someone slide into side and got a little cosmetic damage and I'm money up on car (got more back for it than I paid for car). If it's a cheap simple fix will sort

C3 petrol may have 2 sensors. One for the engine ECU for fan control and the other for dash display.

If you have a faulty dash display temperature sensor it will show hot, when it's not and the cooling fan won't be running.