This paper describes the numerical solution of heat transfer problems using cellular automata. While traditional methods offer high performance on uniprocessor machines, their performance is limited on distributed memory multiprocessors by communication bottlenecks caused by the interdependence of the equations. Using a cellular automata formulation, these bottlenecks can be avoided, and performance greater than that obtained by parallelizing traditional algorithms can be achieved. This paper gives an overview of the cellular automata paradigm and specific examples of solutions to a hyperbolic and a parabolic problem. The accuracy of the method is verified by comparisons of the results with analytical solutions and with results produced by other techniques.