  We study the formation of clusters of galaxies using high-resolution
hydrodynamic cosmological simulations that include the effect of thermal
conduction with an effective isotropic conductivity of 1/3 the classical
Spitzer value. We find that, both for a hot ($T_{\rm ew}\simeq 12$ keV) and
several cold ($T_{\rm ew}\simeq 2$ keV) galaxy clusters, the baryonic fraction
converted into stars does not change significantly when thermal conduction is
included. However, the temperature profiles are modified, particularly in our
simulated hot system, where an extended isothermal core is readily formed. As a
consequence of heat flowing from the inner regions of the cluster both to its
outer parts and into its innermost resolved regions, the entropy profile is
altered as well. This effect is almost negligible for the cold cluster, as
expected based on the strong temperature dependence of the conductivity. Our
results demonstrate that while thermal conduction can have a significant
influence on the properties of the intra--cluster medium of rich galaxy
clusters, it appears unlikely to provide by itself a solution for the
overcooling problem in clusters, or to explain the current discrepancies
between the observed and simulated properties of the intra--cluster medium.
