The equilibrium volume of a thermoresponsive polymer gel changes dramatically across a temperature due to the coil-globule transitions of the polymers. When cofacially oriented nanosheets are embedded in such a gel, the composite gel deforms at the temperature, without changing the volume, and the response time is considerably shorter. We here theoretically predict that the deformation of the composite gel results from the fact that the nanosheets restrain the deformation of some polymers, while other polymers deform relatively freely. The unrestrained polymers collapse due to the coil-globule transitions and this generates the solvent flows to the restrained regions. The response time of this process is rather fast because solvent molecules travel only by the distance of the size of a nanosheet, instead of permeating out to the external solution. This concept may provide insight in the physics of composite gels and the design of thermoresponsive gels of fast response.