I recently changed out my thermostat to a programmable one. It works fine at whatever temp it's set, but it doesn't run the program. I figured it was a problem with the thermostat and went and bought a different model. It's a simple two-wire (heat-only) configuration and I put the appropriate wires in Rh and W. With the new (2nd) thermostat, the heater turns on and doesn't shut off at all. It's not just the blower--it's emitting heat. Any thoughts?

Model of thermostat?
Brand?
Type of heat system?
OIL GAS OE ELECTRIC?

The one that doesn't run the program is a Honeywell RTH230B
The one that runs the heat continuously is a Honeywell
Tempstar Gas Furnace
No idea how old--just moved in a month ago

I would first check to see if the thermostat wires rubbed together or shorted out. A very simple thermostat only makes and breaks a circuit so the thermostat should be OK. You could check the thermostat also with a simple ohm meter. If you remove the wires from the thermostat the unit should shut off unless you have a short in the wiring somewhere.

The instructions for the Honeywell is below.

http://customer.honeywell.com/techlit/pdf/69-0000s/69-1800.pdf

I would put in a brand new set of batteries and then set up the thermostat as the instructions say for your gas furnace. There are a few settings so it should not take to long.

The only other possibility is that a heat relay or other device is stuck on causing the unit to run all time.

It only runs continuously when connected to the one thermostat. It runs okay (sticks to the current temp setting) with the other stat, but doesn't follow the program. Also, it's turning on and off frequently--like for only a minute at a time.