Very hot rooms in Nassau (6)

I believe the answer is:

saunas

I'm a little stuck... Click here to teach me more about this clue!

'very hot rooms' is the definition.
'saunas' can be an answer for 'rooms' (sauna is a kind of room). I'm not certain of the 'very hot' bit.

'nassau' is the wordplay.
'nassau' anagrams to 'SAUNAS'.
But, I'm not clear how the anagram is indicated.

'in' acts as a link.

Can you help me to learn more?

(Other definitions for saunas that I've seen before include "Finnish steam baths" , "Sweat rooms" .)

I've seen this clue in the Sydney Morning Herald.

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