I think ESP8266 is a good option, then you can control and read temperature in the same unit.. Combine that with a 12V relay and you should be good to go.
See my fogmachine setup it’s more or less the same for 12V. Cheap FOG Machine for Halloween controlled by OpenHAB
The shelly route might be simple. A Fibaro RGBW could do the same job (dimming 0-12V).
Regards, S