Every Roman town had its bathhouse.
Inside a Roman Bathhouse by Lawrence Alma-Tadema (public domain photo)
People went there not only to wash and use the toilets but to socialize.
There were halls and dressing rooms and usually three pools of water: A cold one, a lukewarm one, and a hot one. How was the water heated?
There were three bronze boilers in the basement of the building, one on top of another.
A water boiler (miliarium) of the Old Baths at Pompeii from Harpers Dictionary of Classical Antiquities by Harry Thurston Peck (public domain photo)
A fire was started under the lowest one, and the hot water went out through a lead pipe to the calidarium, the pool of hot water.
The caldarium (hot bath) of the Old Baths at Pompeii from Harpers Dictionary of Classical Antiquities by Harry Thurston Peck (public domain photo)
The middle boiler received some of the heat from the one underneath it and sent its water to the tepidarium, the lukewarm pool.
The tepidarium (lukewarm bath) of the Old Baths at Pompeii (public domain photo)
The top boiler with the cold water supplied the frigidarium, the third pool and the one the bathers dipped into first.
The frigidarium (cold bath) of the Old Baths at Pompeii (public domain photo)
The building itself was heated by a system called the hypocaustum.
Baths of Constantine, Arles, France (public domain photo by Rodrigue Eckert)
The floor was two feet off the ground, supported by rows of brick pillars. The hot gases from the fire that heated the water were directed through the space under the floor, up through clay pipes in the walls, and out chimneys in the roof.
Hypocaustum was so successful that it was copied in private mansions like the one in Carranque, Spain, and used all through the Middle Ages. Some rural houses in Castile used this system, which they called a gloria, until recently.
This is an illustration of a hypocaustum, though without the boilers.
Illustration from the catalog of an exhibition at the Museo Arqueológico Nacional, Madrid in March-July 2002 Artifex: Ingeniería Romana en España by Ignacio González Tascón
And this is a photograph of the recent excavations of a huge bath-house at the “lost” Roman town of Clunia, near Aranda de Duero, Spain. Notice the stacks of bricks which supported the hanging floors.
In his treatise on architecture written at the time of Augustus, Vitruvius advises builders to give the ground under the floor a slope towards the furnace, “in such a way that, if a ball is thrown in, it cannot stop inside but must return of itself to the furnace room; thus the heat of the fire will more readily spread under the hanging flooring.”
Main bath at the Roman Baths, Bath, England (Creative Commons Attribution-Share Alike 2.0 Generic license photo by Andrew Dunn)
Remember that public baths are still common in many countries. Here is an old Turkish bath in Budapest, Hungary.
(Creative Commons Attribution-Share Alike 3.0 Unported license photo by uzo19)
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