The timescale of electronic cooling is an important parameter controlling the performance of devices based on quantum materials for optoelectronic, thermoelectric, and thermal management applications. In most conventional materials, cooling proceeds via the emission of phonons, a process that can bottleneck the carrier relaxation dynamics, thus degrading the device performance. Here we present the theory of near-field radiative heat transfer that occurs when a two-dimensional electron system is coupled via the nonretarded Coulomb interaction to a three-dimensional bulk that can behave as a very efficient electronic heat sink. We apply our theory to study the cooling dynamics of surface states of three-dimensional topological insulators and of graphene in proximity to small-gap bulk materials. The “Coulomb cooling” we introduce is alternative to the conventional phonon-mediated cooling, can be very efficient, and can dominate the cooling dynamics under certain circumstances. We show that this cooling mechanism can lead to a sub-picosecond timescale, significantly faster than the cooling dynamics normally observed in Dirac materials.