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The most important thing is to keep the room as cool as possible, heat rises so as long as you have good ventilation at the top of the tank it shouldn't get too bad.
I never put anything from the freezer in the cage or next to the nest/house, if it's very hot I might put a freezer block on a shelf under the cage away from the house so they have a cool spot if they want it but they don't always like it & I don't want to force them out of the house if they don't.
You can put a mug in the fridge then put that in the cage, also tiles or some sand to go in the sand bath, that should be enough.