The temperature dynamics of the radiative heat propagation in a multilayer structure is theoretically treated with a formalism combining the scattering matrix and Green's-functions methods. The time evolution of the temperature of parallel plates of silicon carbide in vacuum is simulated for different interplate distances and thicknesses of plates. The characteristic radiative heat exchange time and temperature of the plates at stationary state are determined from the time evolutions. The threshold interplate distance which separates heating and cooling regimes for the sink plate is found. We show that the variation of the interplate distance allows us to control the relaxation processes in the system of absorber and emitter.