With those types of blocks, it's a cold place in Irish Church building

I believe the answer is:

ice house

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

I don't understand how the rest of the clue works.

(Other definitions for ice house that I've seen before include "Igloo" , "Former cold store" , "Cold storage building" .)

I've seen this clue in the Irish Times.

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