Van der Waals heterostructures have emerged as promising building blocks that offer access to new physics, novel device functionalities and superior electrical and optoelectronic properties(1-7). Applications such as thermal management, photodetection, light emission, data communication, high-speed electronics and light harvesting(8-16) require a thorough understanding of (nanoscale) heat flow. Here, using time-resolved photocurrent measurements, we identify an efficient out-of-plane energy transfer channel, where charge carriers in graphene couple to hyperbolic phonon polaritons(17-19) in the encapsulating layered material. This hyperbolic cooling is particularly efficient, giving picosecond cooling times for hexagonal BN, where the high-momentum hyperbolic phonon polaritons enable efficient near-field energy transfer. We study this heat transfer mechanism using distinct control knobs to vary carrier density and lattice temperature, and find excellent agreement with theory without any adjustable parameters. These insights may lead to the ability to control heat flow in van der Waals heterostructures.