  We present a simple, analytic point source model for both static and
time-varying point-like heat sources and the resulting temperature profile that
solves the heat equation in dimension three. Simple algorithms to detect the
location and spectral content of these sources are developed and numerically
tested using Finite Element Mesh simulations. The resulting framework for heat
source reconstruction problems, which are ill-posed inverse problems, seems
promising and warrants for future research. Possible fields of application for
our work are material testing, to detect manufacturing defects, and medical
imaging to detect abnormal health conditions.
