The addition of a volumetric heat source to a coronal streamer model produces distinct, important changes in the model. Originally, such heating was added to meet the observational requirement for a thin current sheet above streamers. Here we report additional consequences of a volumetric heat source, together with the effects of redistribution of heat through thermal conduction. Specifically, we address the question of whether a heat source will allow a truly steady state to be achieved in the presence of thermal conduction, something known to be impossible for an adiabatic gas. The heat source causes a slow, continuing expansion and stripping of magnetic flux from the top of a streamer until the streamer essentially evaporates and the field is fully open to the interplanetary medium after an interval which depends on the magnitude of the source but typically varies from weeks to months. We find that thermal conduction does not quench the evaporation. We also find that the heat source, in the absence of other processes, must depend on the magnetic field geometry to simulate both the thinness of current sheets above streamers and the low density/high flow speed in coronal holes. Finally, we find that the expansion is not necessarily continuous.¿ 1996 American Geophysical Union