► The Prandtl type operator is used to determine dissipated energy. ► Key equations of the multiaxial operator approach are introduced. ► Operator approach is compared to the traditional integration approach by simulations. ► Integral approach cannot be justified due to cycle identification problem. ► The approach can be used under any rate independent thermomechanical fatigue loading. The paper presents an approach to the energy dissipation calculation under arbitrary multiaxial thermomechanical fatigue (TMF) loading. In such an approach the total area of plastic hysteresis loops is taken as a measure of dissipated energy. The calculation is based on the concept of the developed temperature dependent Prandtl type operator. Energy dissipation is associated to irreversible dislocation movements represented by slider shifts of three independent operators. The dissipated energy is then obtained continuously at any time by collecting dissipated energy increments of each operator. It is shown that the multiaxial operator approach gives us the same total energy of plastic deformation as compared to the classical integration approach. Furthermore, the presented approach enables to automatically split the obtained dissipated energy between the “true” dissipated energy and the elastically “stored” energy. In order to satisfy the request for a minimum number of dedicated material tests, the approach assumes fixed principal directions. Therefore, the proportional as well as non-proportional loading conditions are addressed in the same manner, which is currently the main deficiency of the approach.