I finally, after living here for over two years, decided to install a programmable thermostat.
So I ordered one, and found that the labels on the wires didn't match up. After pulling out the manual and wiring diagrams for the furnace, I realized that I have a two-stage heat pump furnace (heat pump with an auxiliary heat source). The thermostat only supported single-stage heat. Oops. I only wired it up to the aux heat source, so if I kept it I would be running in the less efficient mode all the time. So I pulled off the new thermostat and put the old one back on.
Except when I put the old one back on, it wouldn't turn on. Crap. I tried resetting all the breakers, but nothing. I could see where the AC voltage came into the furnace, went through a transformer, powered the control circuit board, and wires went off to the wall to the thermostat. But I couldn't figure it out. I went to bed and gave up on it.
The next day, I had a few conversations with some handy people in my life. Between those conversations and a Google search, I found that there would likely be a fuse on the circuit board. That evening, sure enough, once I stopped looking at the circuit board as a black box, I saw a fuse. I didn't have a replacement, so a paper clip closed the circuit and I had heat again! (I am lucky that I live on a middle floor and so am not going to be terribly cold without heat.) Lesson learned: turn off the breaker when messing with wiring!
Today I went to Radio Shack and found a replacement fuse. And did some research to find a compatible thermostat, the Honeywell RTH7600D. And also found that the local Home Depot had the thermostat I wanted in stock—right now. So I walked down there and bought it and installed it. It was the last one they had on the shelf.
Now I am very, very excited that tomorrow morning, before I wake up, the furnace will click on and warm the place up. This instead of me getting up and out of bed, quickly hitting the UP button on the thermostat a few times and then quickly hopping back in bed for another thirty minutes.
Oh, and I replaced the air filter, too. I managed to not break anything while I was doing that.