Generally, the most frequently used structural materials are metals which have high strength and stiffness. However, there are many cases, when other important properties come to the fore as well as high deformation by elastic behavior, high viscosity namely good damping effect. The metals do not have these above mentioned properties, but the rubber does. The rubber - thanks to its elastic behavior - is able to establish an elastic connection between hard and brittle structural elements, however, has high load carrying capacity. Vehicle components made of rubber usually exhibit large deformations. Cyclic finite deformations may induce increasing temperature in hyperelastic materials. This case - where changes in deformation and in temperature occur simultaneously - is called coupled thermomechanical problem. Both the mechanical and thermal processes have their own governing equations, that is why special techniques are needed for the computation. A special technique will be presented for solving coupled problems, this is operator split method. The goal of this paper is to show how to solve the coupled thermomechanical problem by the principle of virtual power and the principle of virtual temperature, and how to apply them together.