A self-similar solution for the propagation of a shock wave driven by a cylindrical piston moving according to exponential temporal law in a nonideal rotating gas with heat conduction and radiation heat fluxes is investigated. The density and angular velocity of the ambient medium are assumed to be constant. Heat conduction is expressed in terms of the Fourier law, and radiation is considered to be of diffusion type for an optically thick gray gas model. The thermal conductivity and absorption coefficient are assumed to vary with temperature and density. Similarity solutions are obtained, and the effects of variations in the heat transfer parameters and gas nonidealness on the flow variables in the region behind the shock are investigated.