Suppose you have a cylinder with its surface insulated and there is a partition that is free to move. you put a photon gas on both sides of a partition, and you

Suppose You have a cylinder with its surface insulated and there is a partition that is free to move. You put a photon gas on both sides of a partition, and You have manage to make the temperature of both sides to be different by attaching each side (that is circular cross-section of a cylinder) to the heat bath. The radiation pressure of photon gas depends only on temperature, that implies that there will be different pressure on both side of the partition. So How the equilibrium state will attain if pressure only depends on temperature?