There are currently 23 gay saunas in Bangkok and 8 more in rest of Thailand, and over the years I found 5 normal saunas (for lack of a better name to distinguish them from gay saunas, where sex plays an important part).
New Sathorn Sauna Saphan Khu Alley
13.721939, 100.547510 = 13°43'19.0"N 100°32'51.0"E
I have been once, basic but clean and well maintained. There are signs in Thai language on Sri Bam Pen road, without these I wouldn't have known about this place, about 5 minutes walk from Malaysia hotel, but in a dead-end part of the soi.
Silom Sauna in Soi Sri Bam Pen
13.718827, 100.550534 = 13°43'07.8"N 100°33'01.9"E
I have been once, basic but clean and well maintained.
Entry 200 Baht.
Silom Sauna in Sukhumvit Soi 22
13.725891, 100.565814 = 13°43'33.2"N 100°33'56.9"E
(halfway between Sukumvit road and Rama 4 road)
Entry 200 Baht, open 12-24.
These two are on google maps, but no others of this chain (?).
Language note: silom สีลม sĕe lom means "windmill". Silom road is named after the windmills that used to be there, there is one metal windmill at the canal.
Elsewhere in Thailand
Some Wats have a steam room / herbal steam sauna attached:
Tak Mae Sot Wat Manee Praison วัดมณีไพรสณฑ์
16.717227, 98.573902 = 16°43'02.0"N 98°34'26.1"E
When I passed, I asked for opening times: 1-7 pm.
Pathum Thani Wat Chedi Hoi วัดเจดีย์หอย
14.114025, 100.385188 = 14°06'50.5"N 100°23'06.7"E
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