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In this study, we develop an electro-thermal model to investigate heating and heat dissipation in nanostructured devices. The heating is computed by a drift-diffusion simulation, which accounts for the dissipative transport of charge carriers. The heat dissipation model is based on the phonon Boltzmann transport equation (PBTE). Application of the electrothermal model to a truncated-pyramid-shaped GaN dot embedded in an AlGaN nanocolumn reveals the existence of mesoscopic effects such as a hotspot across the quantum dot and thermal boundary resistances. We enhance the computational efficiency of the thermal model by implementing a coupled PBTE/Fourier model. This method, based on the domain partitioning, provides the same maximum temperature as that computed by the simple PBTE model, resulting, therefore, a powerful scheme for capture local heating effect with relatively low computational effort. Details about the numerical implementation are also provided.