Methyammonium lead tri-halide perovskites (MAPbX3) are highly promising for energy conversion and photonic devices. Here, we present a comprehensive investigation into the temperature (T)-dependent carrier transport, phase transition and photoluminescence properties in single crystals of MAPbI3 (MSC, X = I), with an aim to attain an understanding of the mechanisms governing the carrier motion and phase transition in halide perovskites. We identify a tetragonal to orthorhombic phase at around 150 K. Thermal evolution of the photoluminescent (PL) peak broadening with temperature points to a dominant longitudinal-optical (LO) phonon interaction in MSCs within a wide T-range across two phase transition points. In the tetragonal phase, the hole and electron mobilities in MSC along the direction normal to the main (110) crystallographic plane exhibit an opposite T-coefficient with the one for the holes exhibiting the ∼T-1.6 dependence and that for electrons roughly following the impurity scattering at ∼T1.8. Such distinct behaviours may be understood by the electron traps due to the specific surface conditions in solution-grown MSCs, which tend to play an increasing role at lower T. Thus, seeking viable passivation approaches is critical for the realistic applications of MSCs. These findings enrich the fundamental insight into some key photophysical properties in halide perovskites and can act as a guide for advancing the application of perovskite single crystals targeted at device operation within a wide T-window.