The heated baths of Caracalla in Rome.
This History of Heating timeline from QS Supplies -- a UK company -- dates all the way back to 2,500 B.C.
Lavishly illustrated, it includes examples from modern times, the Middle Ages and Antiquity. For instance, the Romans were big fans of radiant heat:
These systems used by the Romans were hollow spaces below stone floors called the hypocaust. These systems supported the floor on pillars over a chamber with a fire which was lit at one end. Combustion gases passed under the floor to the other side. Newer systems used tile flues or hollow tile walls to conduct heated combustion products. The fire moved from one end to a separate furnace chamber. Later, the hypocaust chamber was eliminated completely and replaced by floor ducts that connected from the furnace to the wall flues.