In this effort we consider damage detection algorithms using thermal probes. The techniques proposed employ models derived from homogenization theory as the model solution in parameter estimation procedures for simulated data for heat flow in a porous medium. We consider data simulated from a model on a perforated domain with isotropic flow and data simulated from a model on a homogeneous domain with anisotropic flow. We report on ordinary least squares methods combined with the method of mappings to detect the presence of damage and to characterize the geometry of the damage.