Look, the relay heats up because it and the surrounding wiring will be
passing 12A at about 0.5 ohms total resistance (including board, screw
terminals, and some wire). That's about 6W dissipated. Relays have no
heatsinks (not the relays you buy off the shelf at least), so they get hot
if small. Solution: large relay. == more money, more noise, and more drive
power. Also larger box. Powering the relay through one of its contacts is
a proven way to build vibrators (as in Tesla coil drivers) because all
sane off the shelf relays break before make, and the relay will never
switch over to the position with the resistor, it will keep falling back
to the NC contact. This will cause arcing on the other contact and maybe
melt the relay if left alone like this.

A goodish relay that does 12A and can be left alone unsupervised for 1
year in a box, without catching fire or melting is not cheaper than $6 in
ones, if you know where to buy it. An optofet should be available for up
to 3 times that much money ($20) if you know where to buy. This will solve
all your problems and comes with UL or CSA or other such compliance so
noone can sue you if it does catch fire after all. It still needs to be
screwed onto a small heatsink, but that is all.

FYI there are a LOT of el cheapo railmount industrial timers and other
items that claim 10 or 16A switching and melt right out of the outer
casing after a year or less of continuous operation. Especially in a hot
and/or wet climate.

It strikes me that one of the failure modes of the relay and/or switch is
to fail closed and if this heater will heat too much it could kill
something. It is up to you to decide whether the something shall be cooked
alive or freeze to death in such an event. If you do not want it cooked,
then you need to add a thermal breaker to the circuit, exposed to the
heat. This is an off the shelf part, that comes specced in degrees C and
Amps. You probably want 15A or 20A and 55 degrees C. This is a little bit
hot for your thermostat range but much better than explaining things to
the firemen imho. There are few if any 45C thermal breakers afaik.

Peter

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