[Luxobarge]

^^^WHS^^^

Especially the coolant temperature sensor, you have classic symptoms of this. Check/clean the connections to it too, not just the sensor itself. The same sensor is used for ECU engine management AND the temperature guage, so if the guage is not reading as it normally would, this is a massive indicator of a fault, but even if it's reading correctly it could still be that.

Baffler's other suggestions are good ones too.

Just one thing - with faults like this, try to test and diagnose thoroughly, rather than just throw parts at it in the hope that something will fix it, because doing this it's all too easy to introduce additional faults.

Yes, we need to know if the EML is on, one way or the other this will include/exclude a number of possible causes. If it's on, you REALLY need to read the codes, this will tell you a lot.