Algorithmic methods for estimating complete temperature fields during hyperthermia treatments based on surface and internal electrical measurements are presented. The techniques utilized draw upon impedance imaging concepts, but rather than limit the measurements to positions on the body surface, internal impedance recording sites are allowed. Theoretical simulations show that this strategy improves the reconstructed image in the target region when either internal measurement locations are added to a given number of external recording sites or some external measurement locations are replaced by internal recording positions. The algorithms developed are tested on a set of problems with increasing levels of complexity. The culmination of these investigations is a complete simulation of a hyperthermia treatment and reconstruction of a thermal image for a body cross-section of an actual cancer patient. The results of this work suggest that the surface plus internal measurement approach holds some promise as a method for estimating temperature distributions during hyperthermia treatments. However, the simulations while promising are idealizations in that they are two-dimensional with modest levels of additive noise. In a companion paper, we explore the viability of this approach in several laboratory phantom experiments which include both static and heat-induced transient electrical property profiles.