id go with the thermostat first then, i had opposite problem with old car wouldnt reach normal temp so thermostat stuck open? only cost £7 for thermostat but £20 for correct red coolant.
fairly easy diy expect wet arm though and note which way round it goes, did mine on my new car when i bought it as i was flushing coolant anyway and it seems a common failure part so didnt want it to fail a few months after flushing system
i replaced sender first and made no difference so put old one back and added new one to my spare part collection, sender is at rear of engine 9opposite side to belts) if you want to change it.
andymac how did it take you 30 mins? 3 coffee breaks?