Vibrational cooling of azulene encapsulated in a hemicarcerand molecular container was studied by pump-probe spectroscopy. Within 1.5 ps of excitation of azulene to the S-1 state, rapid internal conversion through a conical intersection leads to the formation of a vibrationally hot (similar to 1080 K) ground state, the subsequent cooling of which can be monitored by tracking the evolution of the red-shifted hot band at the edge of the ground-state absorption. It was found that the cooling of the hot So state of azulene in the host-guest complex (hemicarceplex) is 2-4 times faster than that in common organic solvents. Such large acceleration points to a high density of matching vibrational modes and efficient mechanical coupling between the guest and the host. The experimental observations were fully corroborated by the results of molecular dynamics simulations.