We have a 3 year old Bryant Oil Furnace, Model 369AAN series "C", that recently started burning up the 120/24 volt coil. The 120/24V coil powers the thermostat. We've burned up two coils within the past two days and am getting ready to repace it for the third time.

You probably have a short in the low voltage wiring. Some wiring probably rubbed through so you need to trace the short down. Start at the thermostat wiring base and work back to the burner.

Like hvac1000 I am assuming that it is the 24 volt side of the transformer that is burning out. If this is true that means that you are drawing too much amperage on the transformer, it could be like HVAC100 said and have a short in the wiring causing the burnout but it could be something else, it is possible that the coil in the gas valve is drawing too many amps for that transformer. Or it could be a combination of two or more things drawing too many amps.

It is possible that the first transformer burned out because of age and when you replaced it you did not get a transformer with the same VA, so check your old transformer, the first one and match the VA of it. It is probably it was a 40 VA and you may have bought a 20 VA, which is not enough. Good luck

letmetellu I think he said it is a oil furnace so it is possible that the safety circuit on the oil burner control is drawing to many VA.

Don't forget to check your voltage input to the transformer just in case. Unlikely the problem but a quick check to be sure. I like the idea of checking your current draw as that would slowly cook it whereas a short would pop it pretty fast. Definitely check the VA rating to be sure its big enough.