A bath where steam is used, similar to a 蒸し風呂. The cross-reference suggests a connection to steam bathing.
See also: 蒸し風呂
I relaxed and sweated in the steam bath at the inn.
hot water bath
A bath filled with hot water, as opposed to a steam bath. This is the more common modern meaning.
On a cold day, I want to soak in a hot water bath.
風呂 is the general term for a bath, while 湯風呂 emphasizes the presence of hot water or steam.
Compound of 湯 (hot water) and 風呂 (bath). The exact historical derivation is uncertain, but the word straightforwardly describes a bath involving hot water or steam.