We use space-resolved dynamic light scattering in the highly multiple scattering regime (Photon Correlation Imaging Diffusing Wave Spectroscopy, PCI-DWS) to investigate temperature-induced phase transitions in polymorphic materials. We study paraffin wax as a simple model system and chocolate, a prototypical example of fat-based products exhibiting complex, history-dependent phase transitions. We find that microscopic dynamics measured using PCI-DWS show remarkable, non-monotonic behavior upon heating: they transiently accelerate when crossing phase transition and slow down above the transition temperature. Sub-micron resolution measurements of the local drift of the sample surface reveal that the speed-up of the dynamics is due to the strain field induced by the change in density at transition temperature. The transition temperatures obtained from PCI-DWS are found to be in excellent agreement with those inferred from complementary differential scanning calorimetry and X-ray scattering experiments, thereby validating PCI-DWS as a new, powerful tool for the characterization of phase transitions in complex soft matter. Finally, we demonstrate the unique possibilities afforded by space-resolved DWS by investigating the spatially heterogeneous response of poorly manufactured or composite chocolate samples.