Hybrid organic-inorganic perovskites are emerging semiconductors for cheap and efficient photovoltaics and light-emitting devices. Different from conventional inorganic semiconductors, hybrid perovskites consist of coexisting organic and inorganic sub-lattices, which present disparate atomic masses and bond strengths. The nanoscopic interpenetration of these disparate components, which lack strong electronic and vibrational coupling, presents fundamental challenges to the understanding of charge and heat dissipation. Here we study phonon population and equilibration processes in methylammonium lead iodide (MAPbI₃) by transiently probing the vibrational modes of the organic sub-lattice following above-bandgap optical excitation. We observe inter-sub-lattice thermal equilibration on timescales ranging from hundreds of picoseconds to a couple of nanoseconds. As supported by a two-temperature model based on first-principles calculations, the slow thermal equilibration is attributable to the sequential phonon populations of the inorganic and organic sub-lattices, respectively. The observed long-lasting thermal non-equilibrium offers insights into thermal transport and heat management of the emergent hybrid material class.