eksponential kurve (thermodynamic heattransportation) (mathmatics)

Hello everyone!

This is my situation:

I have a room, where i know the temperature at this exact moment. (20C).

i have a freezer in the room, this freezer trasports a low amount of cold temperture through the walls, and a high amount of temperture from the compresser (lets just say engine).
what i am trying to do is make a graph of the temperature in the room, when there is no ventilation which means the freezer will increase the rooms temperature.

Now the problem:

The formula for the freezers cold temperatur transportation is dependant on the temperature in the room. (when the room temp rises the amount of warmth transported into the freezer rises)

The compressor on the freezer will turn on every time a set temperature is reached, but this should also increase overtime until its constantly turned on. (at which point it will be throwing ALOT of wartm into the room)

lets assume the room is 100% isolated.

the problem is i dont know how to make a formula that actually depends on another formula, (which then depends on the first)
I.E the freezer temperature is dependant on the room tempeature, but the room temperature is dependant on the freezer compresser, and the compressor is dependant on the temperature in the freezer.

ANY IDEAS HERE WOULD BE AMAZING! dont need a solution just some brainstorming/input on what i could do to get one step closer to a solution, thanks