The aim of this study is to propose a variational method of tolerancing analysis using a multiphysical approach. This method is based on operations on polytopes (Minkowski sum and intersection) and can be used to validate geometric specifications, contact specifications and thermomechanical specifications. The first part describes how thermomechanical strains are integrated into a tolerancing analysis tool, based on operations on polytopes. In the second part correlations are defined between two turbine performance criteria, leakage section and risk of touching, and two geometric conditions respectively. In the third part, the influence of design choices is described, in particular the influence of the shape of the parts and the behaviour of the joints on the thermomechanical operating regime of the turbine. Two turbine architectures are considered in relation to the same two performance criteria, and lastly the main turbine architecture results are discussed and future developments are described.