The friction performance of tread rubber is related to the safety of the vehicle during driving, especially in terms of shifting speeds, cornering, and changing environmental factors. The experimental design used in this paper employed a self-developed automatic multi-working-condition friction tester to investigate the correlation between the friction coefficient of three tread formulations and various factors, including speed, pressure, temperature, side deflection angle, and lateral camber. This experimental study demonstrates that the coefficient of friction decreases with increasing load and increases with increasing sliding velocities due to changes in adhesion friction. Due to the increasing and decreasing changes in rubber adhesion and hysteresis friction caused by temperature, the coefficient of friction shows a tendency to increase and then decrease with the increase in temperature; thus, temperature has an important effect on the coefficient of friction. Based on the basic theory of friction and experimental research, the Dorsch friction model was modified in terms of temperature, and the analytical relationship between the rubber friction coefficient and the combined variables of contact pressure, slip velocity, and temperature was established, which is more in line with the actual situation of rubber friction. The model predictions were compared with the experimental results, and the error accuracy was controlled within 5%. This verifies the accuracy of the model and provides a theoretical basis for the study of rubber friction.