We study the phase-dependent thermal transport of a short temperature-biased Josephson junction based on two-dimensional electron gas (2DEG) with both Rashba and Dresselhaus couplings. Except for thermal equilibrium temperature T, characters of thermal transport can also be manipulated by interaction parameter h0 and the parameter [Formula: see text] . A larger value and a sharper switching behavior of thermal conductance can be obtained if h0 takes suitable values and [Formula: see text] is larger. Finally, we propose a possible experimental setup based on the discussed Josephson junction and find that the temperature of the right superconducting electrode TR is influenced by the same three parameters in a similar way with thermal conductance. This setup may provide a valid method to select moderately-doped 2DEG materials and superconducting electrodes to control the change of temperature and obtain an efficient temperature regulator.