We predict that graphene is a unique system where disorder-assisted scattering (supercollisions) dominates electron-lattice cooling over a wide range of temperatures, up to room temperature. This is so because for momentum-conserving electron-phonon scattering the energy transfer per collision is severely constrained due to a small Fermi surface size. The characteristic T(3) temperature dependence and power-law cooling dynamics provide clear experimental signatures of this new cooling mechanism. The cooling rate can be changed by orders of magnitude by varying the amount of disorder providing means for a variety of new applications that rely on hot-carrier transport.