That heat/RH box turns the fan on whenever the RH or temp rises to the set level. The RH unit is the same as the ones that are used to run bathroom fans but the thermostat is a heat control one or basically works in reverse compared to one that runs your furnace. I took it apart to see what make and model it is and the was no name on it. Had some #s the main one being LR17040 then 10172 150 and tiny ones 94468. An electrical supply or heating/AC shop should have something similar. The speed controller is a general purpose ceiling or paddle fan speed controller and NOT a light dimmer. If you get those units and a double wall plug you could put them all in a four place wall box that would be in the wall of your house. They make plastic ones that would be best but as long as the ground wires are all connected properly a metal one would be fine. I also made a couple of thermostats to control heaters that look just like that speed controller. Just get a baseboard heater thermostat at any place that sells thermostats. I got mine at Canadian Tire.
When I hook up my little electrical meter to the fan with speed controller on it it's 125W at full speed and only 60W at the speed I run it. To mount my fan I screwed two hooks into the ceiling about a foot apart then draped a long blue bungee cord across those hooks and hung the fan from the bungee hooks by the bolt holes on the fan's mounting flange. Can barely tell the fan is running from right outside the door. You can see my dual outlet air pump for the DWC hanging from a long, soft spring as well to dampen sound and keep it off the floor.
L8r