Allan wrote:
We have hive for heating (but they don't appear to have any thermometers
of any sort), and a couple of webcams, so we know if the power goes off
in the whole house or on certain circuits, but it would be nice to get
some warning if the freezer gets too warm (there is a friendly neighbour
who will go in and flick a breaker switch as necessary)

Any recommendations/thoughts?

There are thermometers with wireless sensors, like this:
https://www.amazon.com/AcuRite-00986.../dp/B004QJVU78
(tons of similar things across ebay and amazon)

and some are network accessible:
https://tidbits.com/2018/07/25/wirel...eezer-failure/

I'd probably want one where the sensors speaks wirelessly to some kind of
external box. The sensor itself is thus very low power (small battery) and
doesn't emit any heat to disturb the freezer, while the external box might
take a few watts.

I'd guess the first kind speak basic 433MHz or something similar, and
wouldn't be surprised if someone has reverse engineered the protocol.

Theo