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Thermoresponsive hydrogels have been studied intensively for creating smart drug carriers and controlled drug delivery. Understanding the drug release kinetics and corresponding transport mechanisms of nanoparticles (NPs) in a thermoresponsive hydrogel network is the key to the successful design of a smart drug delivery system. We construct a mesoscopic model of rigid NPs entrapped in a hydrogel network in an aqueous solution, where the hydrogel network is formed by cross-linked semiflexible polymers of PNIPAM. By varying the environmental temperature crossing the lower critical solution temperature of PNIPAM we can significantly change the hydrogel network characteristics. We systematically investigate how the matrix porosity and the nanoparticle size affect the NPs' transport kinetics at different temperatures. Quantitative results on the mean-squared displacement and the van Hove displacement distributions of NPs show that all NPs entrapped in the smart hydrogels undergo subdiffusion at both low and high temperatures. For a coil state, the subdiffusive exponent and the diffusion coefficient of NPs increase due to the increased kinetic energy and the decreased confinement on NPs, while the transport of NPs in the hydrogels can be also enhanced by decreasing the matrix porosity and NPs' size. However, when the solution temperature is increased above the critical temperature, the hydrogel network collapses following the coil-to-globule transition, with the NPs tightly trapped in some local regions inside the hydrogels. Consequently, the NP diffusion coefficient can be reduced by two orders of magnitude, or the diffusion processes can even be completely stopped. These findings provide new insights for designing controlled drug release from stimuli-responsive hydrogels, including autonomously switch on/off drug release to respond to the changes of the local environment.