I have written about this before but now have more info.
When the outside temperature gets below freezing, sometimes when shutting off the car the cooling fan will be running. If it stays cold, and the car cools, it will not start again until the air temp is above freezing. If the car shuts off and the cooling fan does not run, no problem. I replaced the engine temperature sensor with no change. I recently noticed if the fan is running after the car shuts off and I wait about 30 seconds and restart the engine, and let it run for about a minute, the fan shuts off. Then if I shut the engine off it will start fine the next morning no matter how cold it is. Any thoughts, anyone?

 

ECT, there is a chance that you got a bad one. There is also a chance that you have a bad ECU.

 

rspi, I just changed the ECT last fall. Doubtful 2 of them would fail the same way. Where is the ECU located on a 98 V70?

 

Did you change the thermostat when you changed the ECT?