Large (150 km³) magma bodies that contribute to caldera-forming eruptions in the Taupo Volcanic Zone, New Zealand have shown evidence for crystallization and storage on the order of decades to centuries prior to eruption. We compare various conductive and convective heat extraction models to determine which is more likely to enable the heat loss required for short magma storage. We conclude that purely conductive models only account for heat loss on millennial or longer timescales. We also show that convective hydrothermal systems with heat output of 1000 MW in magnitude are required for decadal heat extraction from a large, contiguous magma body; yet, heat output similar to present day conditions would be suitable for cooling magma distributed as a patchwork of smaller magma bodies. This study shows the potential connection with heat flow at the surface and the presence of a magma body, providing future directions for monitoring restless calderas.