All practical cryopreservation protocols require biological tissues to survive two perilous processes: cooling down to cryogenic storage temperature and the subsequent rewarming. In many aspects the threats to cell viability are greater during the rewarming phase. In this paper, we present a new method, which can handle arbitrary structure shapes, for the combined electromagnetic and heat transfer simulation of the microwave rewarming process. In this method, the EM solver is based on the numerical solution of coupled integral equations. It models the cavity wall by a set of small triangles, and represents the dielectric tissue by a set of small tetrahedrons. This model provides the flexibility to simulate realistic cavities and tissue shapes. Since our ultimate interest is in the thermal effect, accurate knowledge of the temperature distribution is crucial to achieve basic understanding, the control, and optimization of the heating processes, This requires the solution of the energy equations within the processed materials. In this paper the control volume method developed by Patankar is used to model heat transfer in biological samples. The inhomogeneous nature of the tissue's electric and physical properties has been considered in the combined analysis.