Frictional contacts of thermoviscoelastic bodies are complicated nonlinear temperature- and time-dependent problems. The introduction of friction with its irreversible character makes the problem more difficult. Additionally, the consideration of temperature, as an independent variable, destroys the convolution integral form of the viscoelasticity constitutive relations. This paper presents a computational model capable of predicting the nonlinear quasistatic response of uncoupled thermoviscoelastic frictional contact problems. The contact problem, as a variational inequality constrained model, is handled by using the Lagrange multiplier method to incorporate the inequality contact constraints. A local nonlinear friction law is adapted to model friction at the contact interface. This, in turn, eliminates difficulties that arise with the application of the classical friction laws. The temperature-dependency of viscoelasticity is modeled by applying the time-temperature superposition principle. The constitutive equations are transformed to be a function of the reduced time as the only independent variable, maintaining the convolution integral form. Two different illustrative examples are presented to demonstrate the applicability of the proposed model to analyze both nonconformal and conformal thermoviscoelastic frictional contact problems.