  This paper analyzes heat equation with memory in the case of kernels that are
linear combinations of Gamma distributions. In this case, it is possible to
rewrite the non-local equation as a local system of partial differential
equations of hyperbolic type. Stability is studied in details by analyzing the
corresponding dispersion relation, providing sufficient stability condition for
the general case and sharp instability thresholds in the case of linear
combination of the first three Gamma functions.
