Microgels are colloidal-scale particles individually made by cross-linked polymer networks, which can swell and deswell in response to external stimuli. The widely studied PNIPAM microgels are nowadays used as model systems for the glass transition. Their dual colloid/polymer nature makes them very interesting because they should undergo two distinct glass transitions, at the level of colloids and of individual chains respectively. While the colloidal glass transition is extensively studied in the literature, the second one has been largely ignored. In a recent proposal, we have started such investigation finding promising results: not only we were able to clearly resolve the occurrence of the volume phase transition in all non-dry samples, but also we detected an interesting phenomenon at low temperatures. Namely, a sharp growth of the elastic incoherent scattering intensity was observed around 250K, suggesting the occurrence of a dynamic transition analogous to that observed for proteins. Here we propose to investigate further such transition at low temperatures and high concentrations and to compare the results with investigations with the chemically analogous macrogels.