In a microwave oven, food is heated as a result of two simultaneous physical processes: absorption of electromagnetic energy (as a result of the transmission of electromagnetic waves), and heat diffusion. It is known from experience that microwave heating can often be very non-uniform and hard to control. A system of coupled partial differential equations modeling these two phenomena is formulated but it is impossible to solve exactly except in trivial cases. We investigate the use of the finite element method software FEMLAB in obtaining numerical solutions to our coupled system. We hope our model aids in designing microwave ovens which have more control over how food is heated.