For the development and design of sound applications, efficient and precise simulations of pieoelectric ceramics are essential. In the small signal range, various simulation tools are available, but those typically only take the linear coupling of electrical and mechanical behaviour into account. When considering higher power levels, thermal properties also play an important role. For that mechanical losses can no longer be neglected, as they have a direct impact on the system temperature. Measurements show that the behavior of piezoceramics changes significantly with changes in temperature \cite{friesen_temp}. The damping approaches known from small-signal behavior still can be used as a basis for further developments. Our simulations have show that changes of the mechanical quantities occur much faster than the thermal state \cite{hoelscher_ICU}. This article deals with self-heating and the associated properties. For this, we developed a multiscale simulation setup in which thermal energy is calculated taking energy conservation into account. Only the dominant mechanical losses are considered. As a further step, the material parameters are updated in the simulation when the temperature exceeds a threshold value. In order to observe a significant temperature increase, a very large number of time steps must be simulated. Therefore, the focus is on multiscale simulation. To this end, various approaches are compared and evaluated with respect to their efficiency. The simulation is implemented using the FEniCS project, which is based on the finite element method (FEM). The aim of this work is to use this open-source framework so that the modifications can be incorporated. Discs and rings are considered as geometries for the piezoceramics. Ring-shaped structures are used in many composite oscillators and are therefore important in practice. An essential aspect is the optimization of computing time, which is why the 3D structure is mapped using 2D simulations that exploit rotational symmetry.