This paper is concerned with the empirical hardening equation of steel sheets for an auto-body at intermediate strain rates with the variation of temperature. In order to identify the temperature dependence of the strain-rate sensitivity of steel sheets such as SPRC35R, SPRC45E and TRIP60, uniaxial tensile tests have been performed with the variation of the strain rate from 0.001/sec to 200/sec and the environmental temperature from $-40^{circ}C$ to $200^{circ}C$. The thermo-mechanical response at the quasi-static state is obtained from static tensile tests and that at the intermediate strain rate is obtained from high speed tensile tests. The effects of both the strain rate and the temperature on the flow stress and the fracture elongation are investigated with the experimental data. Experimental results provide the variation of the strain-rate sensitivity with respect to the temperature. They also show that as the strain rate increases, the variation of flow stress becomes sensitive to the temperature. A phenomenological constitutive model is newly proposed by modifying the well-known Khan-Huang-Liang model. Based on the experimental data, both the strain rate and the temperature dependent sensitivity of the flow stress are considered in the proposed model by coupling the strain, the strain rate and the temperature. In order to verify the accuracy of the proposed model quantitatively, the standard error between the experimental data and the fitted one is compared with other empirical constitutive models such as the Johnson-Cook and the Khan-Huang-Liang models. The comparison demonstrates that the model proposed gives relatively accurate description of the experimental data at the various strain rates and temperatures.