I keep changing the fan setting on my chronotherm IV plus thermostat to auto, yet it changes itself back to on, causing the fan to run continuously. Even when I set the system to "off" and the fan to "auto" it changes itself to "on" and the fan starts up. Is the thermostat defective? If not, how do I get the fan to stay in the "auto" position -- the only way I could get the fan not to run continuously is to pull the thermostat off the wall

Your no exact model number thermostat could have a stuck relay. Some of the Chronotherms use a relay for the blower circuit. If you check all the wiring and nothing is shorted out then it might be thermostat time but without an exact model I cannot look up anything.

I've looked in the user manual and all over the thermostat but the only numbers I can find that may be the model number beyond the name is 32207415-024 0339 but that looks like a serial number. I can change the setting to "auto" and it will turn the fan off, but within a short term it automatically turns itself back to "on" so I don't think the relay is permanently stuck

You could be having a limit problem with the heating unit. Many times if the furnace limit or other control senses a overheat condition it will turn the blower on all by itself. In this case the thermostat will have no control over the blower since the furnace itself is causing the blower to operate.

Label and disconnect the green wire at the furnace low volt terminal strip. The G or Green wire controls the signal from the thermostat to the furnace for A/C and manual blower operation. With the G wire disconnected the blower should not come on with the thermostat set to the OFF position for heat or A/C and also the off or auto position for the fan. This little test may help to isloate your problem. If this does not work then you will need a meter and trace down the offending part.

You did not mention your furnace brand or exact model number so if it has a variable speed motor the test above will usually not work. Good luck.