We present a comprehensive analysis of the out-of-equilibrium Casimir pressure between two high-T c superconducting plates, each kept at a different temperature. Two interaction regimes can be distinguished. While the zero-point energy dominates in the near field, thermal effects become important at large interplate separations causing a drop in the force’s magnitude compared with the usual thermal-equilibrium case. Our detailed calculations highlight the competing role played by propagating and evanescent modes. Moreover, as one of the plates undergoes the superconducting transition, we predict a sudden discontinuity in the force for any plate distance, which has not been previously observed in other systems. The sensitivity of the dielectric function of the high-T c superconductors makes them ideal systems for a possible direct measurement of the out-of-equilibrium Casimir pressure.