Journal bearings operating at high rotational speeds are strongly affected by coupled thermal-mechanical phenomena, making their reliable numerical prediction a challenging task. The viscous shear occurring within the thin lubricant film, whose thickness typically ranges between 5 and 100 \si{\micro\metre}, leads to substantial frictional power losses and therefore constitutes a dominant internal heat source. The resulting temperature rise causes a variation of the lubricant's viscosity and affects the temperature field in the bearing system. The temperatures that occur are of great importance both in terms of their influence on changes in viscosity and in the design of the bearing.\\ In this study, a cylindrical radial journal bearing consisting of a shaft and a bearing shell is analyzed with a focus on the underlying thermodynamic interactions between the solid and fluid domains. A comprehensive thermal model is formulated for the lubricant and the solid domains, enabling the coupled solution of the energy balance and heat conduction equations. To ensure computational efficiency, the \emph{p}-finite element method is adopted and its numerical performance is systematically assessed. Given the convection-dominated nature of the energy equation, a high-order stabilization approach is employed to maintain numerical robustness and accuracy. For this purpose, a SUPG approach is chosen that satisfies the regularity of the order. Compared to spatial discretizations employing linear finite elements or finite volume methods, this allows fewer elements to be selected while maintaining the same level of accuracy.