  I use a simple analytical model to show that simple heat conduction models
cannot significantly suppress cluster cooling flows. I build a static medium
where heat conduction globally balances radiative cooling, and then perturb it.
I show that a perturbation extending over a large fraction of the cooling flow
region will grow to the non-linear regime within a Hubble time. Such
perturbations are reasonable in clusters which frequently experience mergers
and/or AGN activity. This result strengthens previous findings which show that
a steady solution does not exist for a constant heat conduction coefficient.
