right, gonna think, the door has the astronomical/alchemical symbol for mercury (albeit a bit fancier) we have a heater attached firmly to the wall, a tough fridge, a ceiling fan with a switch in reach, a thermostat unconnected to any of these things and a partially hollow solid box, and a light with a switch.
I turn off the light to see if there is another light source then turn it back on if there isn't one
I try sliding the box along the floor, it wasn't said to be secure but it cold be too heavy to lift
The thermostat has to have some way of affecting the room, so I turn it up high and see if the box warms up, that is the only object I can interact with that could be connected