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Context.The interstellar medium contains warm clouds that are embedded in a hot dilute gas produced by supernovae. Because both gas phases are in contact, an interface forms where mass and energy are exchanged. Whether heat conduction leads to evaporation of these clouds or whether condensation dominates has been analytically derived. Both phases behave differently dynamically so that their relative motion has to be taken into account. Aims.Real clouds in static conditions that experience saturated heat conduction are stabilized against evaporation if self-gravity and cooling play a role. Here, we investigte to what extent heat conduction can hamper the dynamical disruption of clouds embedded in a streaming hot plasma. Methods.To examine the evolution of giant molecular clouds in the stream of a hot plasma we performed two-dimensional hydrodynamical simulations that take full account of self-gravity, heating and cooling effects and heat conduction by electrons. We use the thermal conductivity of a fully ionized hydrogen plasma proposed by Spitzer and a saturated heat flux according to Cowie & McKee in regions where the mean free path of the electrons is large compared to the temperature scaleheight. Results.Significant structural and evolutionary differences occur between simulations with and without heat conduction. Dense clouds in pure dynamical models experience dynamical destruction by Kelvin-Helmholtz (KH) instability. In static models heat conduction leads to evaporation of such clouds. Heat conduction acting on clouds in a gas stream smooths out steep temperature and density gradients at the edge of the cloud because the conduction timescale is shorter than the cooling timescale. This diminishes the velocity gradient between the streaming plasma and the cloud, so that the timescale for the onset of KH instabilities increases, and the surface of the cloud becomes less susceptible to KH instabilities. The stabilisation effect of heat conduction against KH instability is more pronounced for smaller and less massive clouds. As in the static case more realistic cloud conditions allow heat conduction to transfer hot material onto the cloud's surface and to mix the accreted gas deeper into the cloud. Conclusions.In contrast to pure dynamical models of clouds in a plasma and to analytical considerations of heat conduction that can evaporate such clouds embedded in a hot plasma, our realistic numerical simulations demonstrate that this destructive effect of KH instability is significantly slowed by heat conduction so that clouds can survive their passage through hot gas.