This manuscript introduces a hybrid approach merging the Alternating Direction Implicit (ADI) method with the Crank Nicolson scheme, renowned for its unconditional stability, for forecasting the thermo-mechanical responses of rubber concrete experiencing thermal shock. Various proportions of rubber aggregate (0%, 10%, 20%, and 30%) are investigated under a constant humidity level (3%). The governing equation for coupled thermo-mechanical phenomena, derived from the heat conduction equation, is delineated, followed by discretization employing the proposed methodology. A comparative analysis between the analytical solution, featuring temperature and time-dependent constants, and the numerical outcomes is conducted to validate the proposed algorithm. Additionally, the impact of temperature on mechanical parameters like tensile strength, compressive strength, and elastic modulus is deliberated. The findings, including 3D contour plots and the temporal evolution of temperature and each mechanical parameter, affirm the capability of our numerical framework in anticipating and scrutinizing the thermo-mechanical dynamics of rubber concrete under fire-induced loading conditions.