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 .