Thermal boundary conditions model the coupling between a convecting magmatic body and its host. Such conditions need to be considered in models of igneous systems that involve thermal histories, crystallization and fractionation of melt, formation of aureoles by contact metamorphism, and any other processes in which transport of heat plays a role. Usually, investigations of magmatic systems have tended to emphasize modeling the interior convective regime relative to treatment of the thermal coupling. Yet it is found that the thermal nature of an intrusion is likely to be influenced more by coupling to its host than by the details of internal convective flows. Evaluation of a parameter having the form of a Biot number (Bi) provides a basis for estimating which boundary conditions are most appropriate. It is found that Bi≤0.1 (constant heat-flux limit) for models of several caldera systems. For such values of the Biot number, the host regime behaves somewhat like a thermos bottle by limiting the flow of heat through the magma-host system so that convective stirring of magma has little effect on the cooling rate of the intrusion. Because of this insulating effect, boundary temperatures assumed in convection models should approach magmatic values even if an active hydrothermal system is present. However, high boundary temperatures do not imply that melting and assimilation of host rock by magma must occur. Despite the thermos bottle effect, magmatic convection can still be quite vigorous.