Hey ang_gl ,
That equation might not work. It doesn't have the time component in it. I know the equation that will be used but am not sure how to implement it. It is the equation you wrote +having q"'/k on LHS equated with (1/alpha)(dT/dt) on the RHS, where q"' is the rate of internal energy...
I have a simplified model (see attached picture) which is part of a bigger model but for now the problem is as follows.
I have a electropolished metal sheet which has spots on it which act as heat sinks because they are kept at constant temperature of 100K. The sheet is at room temperature...