Thermally supported clinching (Hotclinch) is a novel promising process to join dissimilar materials. Here, metal and fibre-reinforced thermoplastics (FRTP) are used within this single step joining process and without the usage of auxiliary parts like screws or rivets. For this purpose, heat is applied to improve the formability of the reinforced thermoplastic. This enables joining of the materials using conventional clinching-tools. Focus of this work is the modelling on mesoscopic scale for the numerical simulation of this process. The FTRP-model takes the material behaviour both of matrix and the fabric reinforced organo-sheet under process temperatures into account. For describing the experimentally observed phenomena such as large deformations, fibre failure and the interactions between matrix and fibres as well as between fibres themselves, the usage of conventional, purely Lagrangian based FEM methods is limited. Therefore, the combination of contact-models with advanced modelling approaches like Arbitrary-Lagrangian-Eulerian (ALE), Coupled-Eulerian-Lagrangian (CEL) and Smooth-ParticleHydrodynamics (SPH) for the numerical simulation of the clinching process are employed. The different approaches are compared with regard to simulation feasibility, robustness and results accuracy. It is shown, that the CEL approach represents the most promising approach to describe the clinching process.