The coolant temperature sensor on a vehicles engine detects the temperature of the engine coolant and tells the computer what temperature the engine is running at.
When a coolant temperature sensor is bad it may cause a lean idle or rough idle and may cause the engine to stall until fully warmed up.
What I experienced with my truck a few years ago when the coolant temperature sensor went bad is I'd have to let the truck run for 15 minutes at idle before I was able to get the engine up to speed and go down the highway.
If I didn't let the engine run for at least 15 minutes the engine would almost always stall or spit and sputter so it was not getting enough fuel.
After I replaced the coolant temperature sensor the engine runs just fine like it should and I can take off within a few minutes of warming the engine up.
I always let the engine warm up for at least a few minutes during cold weather to allow the engine oil to flow through the engine which prolongs the life of the engine.