My ten year old York gas furnace will run fine but intermittently it will not start back up again when the temperature drops. I replaced the thermostat to a Honeywell seven day programmable. That did not fix the problem. If I turn off the furnace at the furnace, wait about ten seconds, and turn it back on, it starts right up. The fuse at the on/off switch looks fine. This furnace does not have air conditioning and I noticed the thermostat only has two wires connecting it to the furnace. Any advise would be greatly appreciated.

I would replace the theromcouple. It is inexpensive, and not to hard. I had a very similar problem and the thermocouple did the trick. I did run into a minor problem, but resolved it fairly easily. The old thermocouple was a little longer than the new one so I had to modify the clip that holds it to get the tip into the pilot light.

If it is working some of the time, I don't think it could be the thermostat.