The bandgaps of CsPbI3 perovskite nanocrystals are measured by absorption spectroscopy at cryogenic temperatures. Anomalous bandgap shifts are observed in CsPbI3 nanocubes and nanoplatelets, which are modeled accurately by bandgap renormalization due to lattice vibrational modes. We find that decreasing dimensionality of the CsPbI3 lattice in nanoplatelets greatly reduces electron-phonon coupling, and dominant out-of-plane quantum confinement results in a homogeneously broadened absorption line shape down to cryogenic temperatures. An absorption tail forms at low-temperatures in CsPbI3 nanocubes, which we attribute to shallow defect states positioned near the valence band edge.