Crossword Genius

Welsh town, without ice, say, getting heated at first (5)

Ross

I believe the answer is:

neath

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'welsh town' is the definition.
(I've seen this before)

'ice say getting heated at first' is the wordplay.
'ice say' becomes 'neat' (I am not sure about this - if you are sure you should believe this answer much more).
'getting' is a charade indicator (letters next to each other).
'at first' says to take the initial letters.
The initial letter of 'heated' is 'h'.
'neat'+'h'='NEATH'

'without' acts as a link.
This may not be correct. It may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for neath that I've seen before include "Under, poetically" , "Town NE of Swansea" , "Welsh rugby club" , "Under (poetic)" , "town in South Wales" .)

I've seen this clue in The Times.
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