Need guidance on simulating my control project
Although you could use just about any program to simulate a thermal system, just make the time steps small in comparison to the temperature change between steps, you can also use programs such as MATLAB (and the free alternatives such as Scilab and Octave) etc. You could even use Excel if you were so inclined.
But I suggest using LTspice, which is freely downloadable. You use analogs for temperature to simulate the thermal aspects (table from this tutorial:

In your system there is no thermal equivalent of inductance, but there are thermal systems where there is.
Of course if you have no idea of what the the parameters are, it will be difficult to come up with realistic simulations but you'll probably learn something in the process and when you get the actual parts you can adjust the parameters to conform to reality (and run tests faster than on real hardware, most likely).