We study the electrophoretic mobility of gold nanoparticles embedded in thermoresponsive poly(N-isopropylacrylamide) (PNIPAM) hydrogels by phase analysis dynamic light scattering (PALS). Approaching the phase transition temperature, the mobility of the nanoparticles strongly increases, which is related to a proceeding spinodal decomposition of the gel into polymer-poor regions and highly cross-linked polymer-rich domains, opening up larger pores which allow for enhanced migration of the embedded tracer particles. This effect, which is also relevant for thermally controlled release of nanoscopic substrates from thermoresponsive hydrogels, is explored in dependence of sample temperature, size of the gold nanoparticles, and structure of the hydrogel (polymer content and cross-linker content).