Last year, we reported on a SPICE-based compact RF small-signal electromechanical model for electrostatically actuated MEMS capacitive shunt switches with movable membranes. We now report on the enhancement of the model to include electrothermal and thermomechanical effects so that the model is applicable under large-signal RF conditions. Specifically, a thermal subcircuit is added to account for the temperature rise in the switch membrane as a function of the dissipated RF power. In turn, the temperature rise is used to evaluate the decrease in the membrane spring constant. These enhancements allow the present multiphysics model to simulate the coupled self-biasing and self-heating effects under RF large signals and to predict the power-handling capacity of MEMS capacitive switches. Additionally, the model has been coded in Verilog, making it portable between different circuit simulation environments.