yes I know there's already thread similar to this but I also have a different problem also.

Before the cold weather... At first the car would idle real low and get really close to dieing and seemed to overheat by the temp gauge. Then I turned up the idle and it idles perfect now when at a stop and doesn't overheat but when ever I put it in neutral it'll go down then come back up to around 1500 then drop to 800rpm-even at normal car temp. Also when I turn on the heater, the temp drops a lot.

Ok now the cold weather...the car takes forever to warm and doesn't warm up fully even after driving. And still having the same heater problem where the temp will drop a lot.

 

in addition to replacing the thermostat i'd replace the temp sender.

 

Check your coolant level.
Check your thermostat.