The deformation experienced by solid propellant grain after the curing cooling process may lead to structural failure. To solve such finite deformation, we introduce a meshless approach called Deep Learning Energy Method (DLEM), also known as a kind of Physics-Informed Neural Networks (PINNs). Firstly, the governing equation, strain energy density function and potential energy expressions of hyperelasticity and thermo-hyperelasticity are provided. Secondly, a deep neural network is employed to represent the deformation field, allowing to minimize the potential energy of the structure by training the neural network. To validate the effectiveness of DLEM, we successfully solve the deformation of a cube under 0.5 MPa. Furthermore, we apply DLEM to analyze the deformation of typical tube grain and slot grain after the curing cooling process, where the temperature decreases from 75 °C to 20 °C. The results reveal deformation distribution near the inner surface of the tube and slot, which aligns well with results obtained by finite element method. This research presents the first application of DLEM to thermo-hyperelasticity. As a kind of meshless methods and energy methods, it is especially suitable for treating complex geometry and boundary, providing a promising pathway for addressing the thermo-hyperelastic finite deformation challenges encountered in designing complex propellant grains.