The town Bath, England has 3 natural hot springs. The Romans built a place of worship and a Thermae around the springs. Why did the Bath need a [Hypocaust][1] if the water was already 47C hot just from the geothermal energy? What water did they use for the frigidarium and the other cold bath?

Take a look at the plans of the West Baths of Bath \[citation needed\]. There's a Hypocaust system under the Tepidarium, the warm bath indicating that the Hypocaust was not only there to warm the floor but to also heat the water. Beyond that, as far as i know there were some Hypocaust system where the water tank was built above the praefurnium to also directly heat the water. 


  [1]: https://en.wikipedia.org/wiki/Hypocaust