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Nonpneumatic tires made from materials with a low viscoelastic energy loss can be an option for developing tires with a low rolling resistance. For better fuel-efficient design of nonpneumatic tires, the rolling energy loss of the nonpneumatic tires may need to be analyzed at a component level. The objective of this study is to develop a numerical tool that can quantify the rolling energy loss and the corresponding internal heat generation of a nonpneumatic tire. We construct a thermomechanical model that covers the interaction between the deformation and the related heat generation in an elastomer material. We suggest, for various vehicle loads and various rolling speeds, a coupled thermoviscoelastic material model for a nonpneumatic tire with a hexagonal cellular spoke in order to investigate the temperature distribution of the nopneumatic tire generated by hysteresis and convection loss to the air. Using a hyperviscoelastic material model developed from uniaxial (tension and compression) tests and dynamic mechanical analysis, a thermomechanical model is constructed by combining a shear-deformation-induced hysteresis and a cooling procedure when exposed to the air. The model of the temperature rise of the nonpneumatic tire is validated using temperature measurement with a thermal imaging camera during rolling of the nonpneumatic tire. The developed tool combining the viscoelastic material model with the aerodynamic heat loss quantifies well the hysteretic energy loss and the temperature distribution at each component of the nonpneumatic tire.