Heat funnction in steady state

balulu

I was given the following interesting question.

A closed room contains several identical machines in it, they are fed by an electrical cable.
The machines can be turned on or off. When a machine is turned on, it consumes electrical energy and as a by product generates heat. The heat is radiated through the room walls to the outside air.
What is the function that describes the room surface temperature in steady state as a function of the number of machines that are turned on? Is it power 2 or 3 of β (the number of machines that are turned on)?

In order to simplify the analysis you can assume that the room is a ball.