Our work has been focused on developing a methodology for process control of bulk deformation-specifically, extrusion. A process model is required for control. The difficulties with currently available models are stated. An appropriate decomposition and associated assumptions are introduced, permitting construction a real-time process model via spectral approximation to solve the axi-symmetric, 2D transient heat conduction equation with heat generation and loss. This solution, simulation results, and model execution times are provided.