Poly(N-isopropylacrylamide) rnicrogels were coassembled with Au nanoparticles into disordered glassy phases and irradiated with a tightly focused laser (lambda = 532 nm) to study crystallization dynamics following a localized photothermal annealing process. The degree of crystallization produced by the annealing process is dependent upon heat flux into the sample at the site of irradiation, the length of irradiation time, and the temperature of the surrounding bulk assembly that functions as a quenching bath. Control over these sample conditions provides a method by which to probe the dynamics of crystallization over a set of microgel concentrations. The mobility, and thus the crystallization, of particles is shown to be frustrated as the microgel concentration is increased. This is in contrast with equilibrium experiments that have shown an increase in particle mobility with microgel concentration that is manifest as an increase in the freezing transition of the bulk assembly with increasing packing density.