Cooler running tires with a reduced rolling resistance is a consideration for both tire makers and automotive original equipment manufacturers. To investigate the mechanics of energy loss and temperature rise, a nonlinear viscoelastic model suitable for numerical analysis of rolling tires is developed and demonstrated. The rubber compounds are represented as nonlinear viscoelastic materials with temperature and frequency, strain, and strain history–dependent response. Several applications to different tire designs are provided to demonstrate the impact of this new material constitutive law in improving the quality of the numerical predictions over other methods. One application is a rolling tire model that was used to delineate the tire temperature distribution and the resultant rolling resistance for different three-dimensional tread patterns.