In this paper, we present an implicit formulation of peridynamic theory for coupled thermomechanical problem based on the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework, with special application to the simulation of fracture behavior of nuclear fuels at high temperature. First, the coupled peridynamic thermomechanical model is briefly reviewed. Next, an implicit formulation for the solution of static or quasi-static problems is proposed. Finally, the formulation is verified against benchmark solutions for both elasticity and heat conduction problems. The nuclear fuel fracture problems is modeled using the proposed implicit scheme. The mesh dependencies of crack initiation are also investigated.