In this Letter, we investigate the temperature dependence of the optical properties of methylammonium lead iodide (MAPbI₃ = CH₃NH₃PbI₃) from room temperature to 6 K. In both the tetragonal (T > 163 K) and the orthorhombic (T < 163 K) phases of MAPbI₃, the band gap (from both absorption and photoluminescence (PL) measurements) decreases with decrease in temperature, in contrast to what is normally seen for many inorganic semiconductors, such as Si, GaAs, GaN, etc. We show that in the perovskites reported here, the temperature coefficient of thermal expansion is large and accounts for the positive temperature coefficient of the band gap. A detailed analysis of the exciton line width allows us to distinguish between static and dynamic disorder. The low-energy tail of the exciton absorption is reminiscent of Urbach absorption. The Urbach energy is a measure of the disorder, which is modeled using thermal and static disorder for both the phases separately. The static disorder component, manifested in the exciton line width at low temperature, is small. Above 60 K, thermal disorder increases the line width. Both these features are a measure of the high crystal quality and low disorder of the perovskite films even though they are produced from solution.