Archnet.org. Search: hammam (bathhouse)

"The portal of Amir Bashtak's hammam is the only surviving remnant from the original Mamluk bath. Now located about one and a half meters below ground level, the portal has a ribbed keel arch with the amir's blazon (a napkin, the blazon of the jamdar, or master of the robes), inlaid black & white marble strapwork, and a dated inscription. The interior, likely remodeled during the Ottoman period, retains many typical elements of bathhouse design. It may have originally been a double bath for men and women, but only one half survives; the men's half was in use until the early years of the 21st century, providing bathing facilities for people of the lower and middle classes who lived nearby.

Sources:

Warner, Nicholas. The monuments of historic Cairo: a map and descriptive catalogue, 133. Cairo: American University in Cairo Press, 2005.

Williams, Caroline. Islamic monuments in Cairo : the practical guide, 93. Cairo: American University in Cairo Press, 2008.

Levels in Q's post regarding Epstein's temple. If it is a bathhouse, then one of the lower levels would be the hammam.

Reading on archnet.org seems that some are public and above ground and some below with more private areas.

The "gym" article Q posted mentioned "grotto" which indicates private and also immediately made me think playboy mansion. Was it a bathhouse/shrine as well?

Grotto: an artificial recess or structure made to resemble a natural cave

Interesting example provided by Miriam-Webster:

Examples of grotto in a Sentence

at the heart of the shrine is a small rocky grotto into which pilgrims can descend

"Blazon of Jamdar" marks the Mamluk bath from what I'm gathering. Blazon = napkin = handkerchief…. surely not Skippy related?

Anyway, treasure grove of information there and it isnt phone friendly. So moar eyes would be good.