Halide perovskites show unusual thermalization kinetics for above-bandgap photoexcitation. We explain this as a consequence of excess energy being deposited into discrete large polaron states. The crossover between low-fluence and high-fluence "phonon bottleneck" cooling is due to a Mott transition where the polarons overlap (n ≥ 1018 cm-3) and the phonon subpopulations are shared. We calculate the initial rate of cooling (thermalization) from the scattering time in the Fröhlich polaron model to be 78 meV ps-1 for CH3NH3PbI3. This rapid initial thermalization involves heat transfer into optical phonon modes coupled by a polar dielectric interaction. Further cooling to equilibrium over hundreds of picoseconds is limited by the ultralow thermal conductivity of the perovskite lattice.