I use one of these on heat tape to keep a pipe in the garage from freezing. Problem is the WIDE temperature range. If you're controlling a space heater, that can use up a lot of juice getting to 45. Also, it reacts to the air temperature. I was interested in the pipe temperature under the insulation.
I experimented a LOT with an economical way to keep the pipe from freezing. Spoiler alert...I finally decided that it was too much hassle and switched to the above-mentioned plug/thermostat. The heat tape is PTC, so it draws little current when it heats up.
I experimented a lot with coiled bi-metalic thermostats. By the time I got them loose enough to work near freezing, the adjustment was so fiddly that I couldn't get it to stay where I wanted. Just too much risk of the pipe freezing.
What did work it this:
I just stuck the sensor under the pipe insulation and used it to control power to the heat tape. Very tight hysteresis. I mounted into a 2-wide duplex box along with a duplex outlet. Runs off a 12V wall wart.
Relay is rated at 10 amps, so may have to add another relay if your heater takes more than that.