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I'm looking to put a Tellstick Net as a remote for my electric heating system in a during-the-winter-unheated house. Could anyone tell whether it is a suitable device for that? Let's say, can it work in temperatures around -20 celsius?

-20 C seems quit low for consumer grade equipment. I don't think the Tellstick units were designed for use in such low temperature ranges.
You should also consider how the rest of the equipment (router/modem/remote switches) behaves in - 20.

Perhaps you could put the Net in an insulated (frigolite) box and hope that the generated heat keeps the unit working.

I use my in the same temperature, winter can be down to minus 20. No problem so far...