Accurately predicting the effective behaviour of materials with complex microstructures remains a significant challenge in materials science and engineering. In particular, the inherent interplay between electricity and temperature, significantly influenced by Joule heating and temperature-dependent material properties, necessitates a comprehensive multiscale modelling approach for accurate predictions of the thermo-electrically coupled response of heterogeneous materials. Combining Hill–Mandel-type energy-equivalence principles, formal two-scale asymptotic expansions, and rigorous two-scale convergence, we derive effective macroscopic field equations that capture the nonlinear interplay between thermal and electrical fields in periodic heterogeneous media. This formulation reflects the strong coupling by means of dissipative processes at the macroscale that are driven by the underlying microstructure. A rigorous mathematical foundation for the coupled multiscale system is presented using two-scale convergence analysis. This analysis confirms the validity of commonly used engineering assumptions in asymptotic and Hill–Mandel-type approaches. The applicability of the proposed framework is demonstrated through a selection of canonical examples. A (quasi-)one-dimensional two-phase laminate is used to introduce key concepts and to provide analytical expressions for effective conductivities. In a second step, the analysis is extended to two-dimensional configurations including checkerboard microstructures and circular inclusions, with the influence of the microscale geometry on the homogenised thermal and electrical properties being explored. Across all examples, we demonstrate how microscale dissipation and coupling phenomena manifest themselves at the macroscale, providing both physical insights and computationally efficient formulations.