Electrical connectors are widely used in electromechanical equipment. Their rough surfaces inevitably induce electrical contact resistance (ECR) and thermal contact resistance (TCR), which generates a significant influence on electricity and heat conducting at the faying surface and affects the accuracy of the thermal-electrical-mechanical coupling (TEMC) numerical calculation. Thus, a TEMC model with ECR and TCR of a parallel groove clamp is necessary to investigate the TEMC mechanism. Firstly, appropriate ECR and TCR models are created based on the available experimental results. Secondly, a refined TEMC finite element model is established by optimising the mesh size at the faying surfaces, and the cyclic coupling calculation method is adopted to achieve efficient and consistent numerical calculations. Meanwhile, the validity of the simulation model is verified by experimental results. Finally, the transient real contact area, current density, and heat generation rate (HGR) are obtained to analyse the TEMC mechanism during temperature rise. The results indicate that the mechanical characteristics during temperature rise are different under two loading conditions of tight and loose, thereby resulting in different changing laws in terms of the maximum current density and HGR. In addition, two coupling mechanisms exist until the steady-state temperature is achieved.