Thermal conduction plays an important role in the
dispersal of energy in supernova remnants and also in the interstellar
medium at large. It can indeed become strongly anisotropic in
the presence of magnetic fields. While the problem has been formulated
and studied by theorists, the effect of thermal conduction has
not been incorporated into large scale simulations, perhaps because
of the difficulty of the operators involved. In this talk we formulate
the problem numerically and apply it to the evolution of SNRs
which play an important role in the evolution of the ISM. It is
shown that the temperature in the hot gas bubble of a SNR as well
as the emissivity in high-stage ions is strongly influenced by
the inclusion of thermal conduction. We, therefore, conclude that
extracting observable diagnostics is risky when thermal conduction
is excluded in large scale Galactic and proto-Galactic simulations.