Installing new 2-wire (Single Pole) Thermostats - how to install when there are 3 wires in wall?
The thermostat is really just a switch that opens and closes (that is, turns power on and turns power off) when the temperature changes.  The wiring in your picture would likely indicate one supply switching what ever is downstream on two wires.  That's consistent with your setup, where it's set to switch the heater and the fan together.
It's important that the thermostat be rated for the current and power use of the loads that it switches.  You'd want to be very careful that your new thermostat can handle at least as much as the one you're replacing (assuming the original was sized correctly).
But if the switching the two devices was OK before, it should be OK with the new thermostat installed - it's a simple two wire device and although the logic controlling it may be more sophisticated it, ultimately it's function is exactly the same:  it's opening and closing a switch.
It doesn't matter which of the two black wires from the thermostat you connect to the single wire, and which to the other two.  The important thing is you keep the two that are under the tan wire nut with the red lead from the old thermostat together.