<p>In this paper, we develop a multiphysics finite element method for a thermo-poroelasticity model with nonlinear permeability. To reveal the multi-physical processes of deformation, diffusion and heat transfer and propose a stable numerical scheme, we reformulate the original model into a fluid coupled problem–general Stokes equations coupled with two diffusion equations. Then we propose a fully discrete finite element method which can use arbitrary finite element pair for space discretization. And we give the stability analysis of the above proposed method and prove that the fully discrete multiphysics finite element method has an optimal convergence order. Also we give some numerical examples to show that the proposed method is consistent with the theoretical results and it can achieve good results for different finite element pairs. Finally, we draw conclusions to summarize the main results of this paper.</p>