  We simulate the evolution of cluster galaxies' hot interstellar medium (ISM)
gas due to ram pressure and thermal conduction in the intracluster medium
(ICM). At the density and temperature of the ICM, the mean free paths of ICM
electrons are comparable to the sizes of galaxies, therefore electrons can
efficiently transport heat due to thermal conduction from the hot ICM to the
cooler ISM. Galaxies consisting of dark matter halos and hot gas coronae are
embedded in an ICM-like `wind tunnel' in our simulations. In this paper, we
assume that thermal conduction is isotropic and include the effects of
saturation. We find that as heat is transferred from the ICM to the ISM, the
cooler denser ISM expands and evaporates. This process is significantly faster
than gas loss due to ram pressure stripping; for our standard model galaxy the
evaporation time is $160$ Myr while the ram pressure stripping timescale is
$2.5$ Gyr. Thermal conduction also suppresses the formation of shear
instabilities, and there are no stripped ISM tails since the ISM evaporates
before tails can form. Observations of long-lived X-ray emitting coronae and
ram pressure stripped X-ray tails in galaxies in group and cluster environments
therefore require that thermal conduction is suppressed or offset by some
additional physical process. The most likely process is anisotropic thermal
conduction due to magnetic fields in the ISM and ICM, which we simulate and
study in the next paper in this series.
