It’s detective time! What was the thermostat that being used? What was the source of power being used by the thermostat? Was there any service type work done at the house, days before?
This looks like one of those rooms over a garage! With the several cold spells we’ve had lately, this along could stress on any open connections like a low voltage transformer, exposure for hours and then shout off to not so much as a heated space tempered but stabilized to a temperature difference of thirty degrees and even more.
Note that the smoke damage is at the baseboard. Granted smoke will pour out of any orifice with enough pressure but if the toe board is burnt or charred there is a clue.
The heating unit needs to be inspected! The transformer of the that unit or the house hold bell ringing transformer if it is supplying the source of power should also be checked.
If battery is the only source than that model should be invested;
thermostat battery failure.
Maybe someone could proof an equation to show how the voltage could get that high off of a 12v or 24v transformer. If not, use
this link to input the basic numbers two numbers and keep the work range of 18 AWG in mind when you increase the voltage.
I would certainly use a meggar for this room and the room connected.
I'd have them remove the sheet rock to the toe board. Maybe even the wall below. great application of a snake light!
Maybe new circuit, truely new LV wire, and new thermostat! Guess it all depends on what all the facts are!
Hope I didn’t kill your thread!