Based on the metal-insulator transition of two phase-change materials (PCMs) with asymmetric thermal conductivities and emissivities sensitive to temperature, a radiative thermostat capable of maintaining a constant temperature without consuming energy is proposed. This is done by deriving explicit expressions for the heat flux and temperature profiles of the thermostat surrounded by these PCMs, and demonstrating that the thermostat can be maintained at a temperature nearly equal to the common transition temperature of both PCMs as the environmental temperature changes by more than 20 K. I show that the combined operation of two PCMs is much better than two non-PCMs to develop energy-free thermostats, especially those supporting poor thermal conduction or dominant heat radiation. The obtained results thus establish a fundamental theoretical method that exploits the nonlinear heat transport driven by electrons, phonons, and photons to maximize temperature preservation and thermal insulation.