bad idle, variable to temp outside

[Pimpin Dsmstyle]

My car runs like shit until it gets to temp, then it runs fine, but surges. The surge is weird because sometimes it is from 1k-1.5k, sometimes 2k-2.2k etc. Really changes. I noticed that below zero its ALWAYS around 2k surge. When its around 20 out, it stays below 1.5k. Every once in a while, I get a coolant light popping on. I pour a little in and it goes away. THIS ONLY HAPPENS WHEN IT SITS OUTSIDE IN THE FREEZING COLD OVER NIGHT. This does not happen when it sits in the garage. My question is this, could the coolant temp sensor cause this problem? I do not get a CEL at all. Thanks.