The algorithm used is the explicit forward-in-time method. For this method to be stable on this grid, the time increment must be less than 0.25.

Experiment with time increments larger than 0.25 and then see if you can regain control of the algorithm once an instability has manifested itself. Note: Subsequent to the appearance of an instability, time-accuracy of the model is lost. You may still be able to get the algorithm to reach a valid steady state temperature distribution.