2001 Ford Focus Replacing Thermostat

So about a couple of weeks ago I was driving home and my car over heated and gave me the warning light and such. I pulled into a gas station (after sitting on the side of the road for 20 minutes letting it cool down) and noticed the anti-freeze was empty. I purchased some anti-freeze at the gas station filled it up to the line and everything worked fine. Or at least I thought.

Last week it got cold enough around here to turn on the heat in my car when driving to work in the morning. I turned it on only to notice it had very spotty performance, sometimes I would get heat, and sometimes I would get cold air but mostly cold air. In order to avoid cold air (no air is better then cold air on a cold day) I just turned off the AC/Heat.

While driving into work this morning, I noticed my car heat level was very high so I cranked up the heater to help it get rid of the heat and noticed it ran hot for only about 1 minute before giving me cold air, and continued with the spotty performance until I reached work (the temperature stayed right below the red line).

When I reached work I opened the hood and noticed I was again out of anti-freeze (even though I replaced it less then a month ago).

So I know nothing about cars, but I'm thinking the thermostat might be getting stuck and thats why I'm getting the cold air. And then when it is stuck it is causing the anti-freeze to boil away?

Therefore I'm hoping this problem is the thermostat and I can just replace that this weekend and have it resolved. I was hoping someone might be able to tell me how to do that, and if this could also be another problem that is not the thermostat.

I'm really really really trying not to purchase another car.

Thanks