Not knowing what type of heater it is, Ill ask a dumb question. Does it have a fan motor?
The answer to your basic question is, yes some AC devices will work on DC, and some DC devices will work on AC. Having said that, it is important to eximine each component to see that it is compatable. (switches, relays, motors, coils, SCR's, and surge protection equipment). Even things as small as fuses can be sensitive to being DC operated.