I don't think they have quoted you for the right sensor, I'm sure its more expensive than that, its the 4 pin one located in the plastic flange on the front of the head. I think its this one:
6U0 919 501 B - temperature sender for coolant temperature gauge and electronic control unit - £22.37
Edit: Thermostat is a good plan, but it wont have anything to do with your starting problems
