Temperature gauge
 

I replaced my coolant temp sensor yesterday in hopes that this would solve my temperature gauge not moving. Well it hasnt seemed to help that much. It will sometimes go to 1/4th of the gauge then drop back down to cold. Whats weird is after the car has been driven and is warm, i turn it off to maybe run into a store or something and when i go to start the car the gauge is in the middle where it should be but after 20-30 seconds it will drop back down to cold. Also sometimes the car will not cold idle (1500 rpm warm up) even when its been sitting overnight in cold temperatures. I have to throw in, this whole gauge situation started occouring after a major coolant leak that took place weeks ago. What could be the problem since I replaced the Temp sensor. Stuck thermostat?

Thermostat would be the next reasonable try. It's a cheap job if you're able to capture all the coolant and reuse it. Not sure that a bad thermostat would cause cold start problems but it's worth a try anyways.