The temperature distributions in overdriven steady wave fronts in 2024 Al shocked up to 80 GPa were predicted using the thermoelastic theory (Wallace theory), where the viscous stress is neglected, and the thermoviscous theory (Sano-Abe theory). The Wallace theory was improved by applying a more exact equation to the bulk modulus. As shock loading was increased, the difference between the temperature distributions predicted using each theory was greater. This tendency of the difference was similar for shocks up to 250 GPa in Pt. Thus, temperature distributions in overdriven steady wave fronts cannot be effectively evaluated using thermoelastic theory.