>>16903528
>500k
500,000 celcius or 500 kelvin?

>>16903528
This is a pretty nonsensical question, it's missing several details like what is the composition of the hypothetical sphere and the room. Other than that it's pretty simple thermal equalization calculation.

>>16903537
500 keV

You would need the value for the heat capacity of the material. You also need to know what temperature you are starting at.

>>16903528
>want to test it with extreme values
Theories and mathematical equations usually come apart at extreme values because some normally negligible effects suddenly have a more significant influence.

And like the other anons said, you need to define a material. Although at very high temperatures you usually deal with some sort of plasma.

>>16903528
surface of sphere = 4 * pi * R^2
Stefan Boltzman law: M = alpha * T^4
where alfa is the stefan boltzman constant and M is watts per square meter

>>16903528
Depending on the material, size and temperature you will know how much energy you can store in that sphere.
Depending on the amount of energy required to maintain the temperature constant at the desired level you can have an idea of how big it should be.