  Thermal conduction in the intracluster medium has been proposed as a possible
heating mechanism for offsetting central cooling losses in rich clusters of
galaxies. In this study, we introduce a new formalism to model conduction in a
diffuse ionised plasma using smoothed particle hydrodynamics (SPH), and we
implement it in the parallel TreePM/SPH-code GADGET-2. We consider only
isotropic conduction and assume that magnetic suppression can be described in
terms of an effective conductivity, taken as a fixed fraction of the
temperature-dependent Spitzer rate. We also account for saturation effects in
low-density gas. Our formulation manifestly conserves thermal energy even for
individual and adaptive timesteps, and is stable in the presence of small-scale
temperature noise. This allows us to evolve the thermal diffusion equation with
an explicit time integration scheme along with the ordinary hydrodynamics. We
use a series of simple test problems to demonstrate the robustness and accuracy
of our method. We then apply our code to spherically symmetric realizations of
clusters, constructed under the assumptions of hydrostatic equilibrium and a
local balance between conduction and radiative cooling. While we confirm that
conduction can efficiently suppress cooling flows for an extended period of
time in these isolated systems, we do not find a similarly strong effect in a
first set of clusters formed in self-consistent cosmological simulations.
However, their temperature profiles are significantly altered by conduction, as
is the X-ray luminosity.
