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Extreme power dissipation would keep temperature stable so that this whole setup might not be needed, though.

Author should experiment with liquid nitrogen ;) [1]

The timing crystals don't work better when colder but worse. That's why they are heated in high end time appliances, not cooled.

Isn't the issue here temperature stability? (Also, humour)

Right, and they are heated because a hot wire is much simpler than a fridge.