Past climates, such as the Eocene (55 - 38 Ma), experienced dramatically warmer polar winters. Global climate models run with Eocene-like boundary conditions have under-predicted polar temperatures, a discrepancy which has stimulated a recent hypothesis that polar stratospheric clouds may have been important. We propose that such clouds form in response to higher CO2 via changes in stratospheric circulation and water content. We show that the absence of this mechanism from models of Eocene climate may be attributable to poor vertical resolution in the neighborhood of the tropical tropopause. This may cause the models to underestimate future greenhouse warming.