We present an approach to performing rapid calculations of temperature within tissue by interleaving, at regular time intervals, 1) an analytical solution to the Pennes (or other desired) bioheat equation excluding the term for thermal conduction and 2) application of a spatial filter to approximate the effects of thermal conduction. Here, the basic approach is presented with attention to filter design. The method is applied to a few different cases relevant to magnetic resonance imaging, and results are compared to those from a full finite-difference (FD) implementation of the Pennes bioheat equation. It is seen that results of the proposed method are in reasonable agreement with those of the FD approach, with about 15% difference in the calculated maximum temperature increase, but are calculated in a fraction of the time, requiring less than 2% of the calculation time for the FD approach in the cases evaluated.