A key invention in the history of baths was the hypocaust which was invented at the end of the 2nd century BC. Though evidence of the floor heating systems exists in earlier models, it seems that the Romans really developed and perfected this technology.
Who invented hypocaust?
SERGIUS ORATA: INVENTOR OF THE HYPOCAUST? current reference, cf. Appendix, no. 1.
Did the Romans invent hypocaust?
Under floor heating invented by Romans
The earliest known record of an underfloor heating system was in ancient Rome. The Romans built this heating system called hypocaust for heat distribution. It was the forerunner of the present day heating systems and ahead of its time.