Intraband relaxation in polycrystalline films of hybrid perovskites methylammonium lead tribromide and methylammonium lead triiodide are studied by transient absorption spectroscopy from 80 K to >350 K. This temperature range spans the transitions of these materials from the high-temperature cubic phases, intermediate tetragonal phases, and low-temperature orthorhombic phases. The organic cation undergoes a distinct transition from an ordered lattice in the orthorhombic phase to a plastic crystal in cubic and tetragonal phases, which reportedly influences many optoelectronic properties. The much larger exciton binding energy of orthorhombic MAPbI3 (compared to cubic or tetragonal phases) or MAPbBr3 substantially changes the transient spectral responses of the materials by reducing the number of free carriers. However, for these measurements at low fluences, both MAPbBr3 and MAPbI3 exhibit subpicosecond intraband relaxation over the entire temperature range studied. Intraband relaxation becomes somewhat faster at higher temperatures, but freezing of organic cations are not accompanied by a discontinuity of the intraband relaxation time. These results suggest that configurational freedom of organic cations does not screen carriers from electron-phonon coupling.