The influence of thermal stress during hydraulic fracturing in deep shale reservoirs cannot be neglected, and the mechanism of fracture height propagation under the combined effects of thermal stress and bedding planes remains unclear. The continuous-discontinuous element method was used to develop a three-dimensional thermo-hydro-mechanical coupled hydraulic fracturing model (CDEM-THM) to investigate the fracture height growth mechanisms and hydraulic fracture-bedding plane interaction behaviors under the combined effects of thermal stress, vertical stress difference, and bedding plane cohesion. The results show that thermal stress significantly alters the original in-situ stress field and serves as a key factor controlling fracture height growth and the interaction mode between hydraulic fractures and bedding planes. By acting as tensile stress, thermal stress reduces the three in-situ principal stresses and lowers the fracturing pressure, resulting in increased fracture width, reduced fracture height and length, and the generation of secondary fractures. Thermal stress reduces the normal stress above bedding planes, thereby lowering the activation difficulty and enabling hydraulic fractures to activate parts of the bedding planes while crossing them. When the vertical stress difference is small, the promoting effect of thermal stress on the fracture's ability to cross bedding planes becomes more pronounced, causing the interaction mode to evolve from propagation along bedding planes to partial activation and crossing. In reservoirs with high temperatures and thermal expansion coefficients, the generated high thermal stress plays a positive role in the vertical extension of fracture and the formation of complex fracture networks. A larger vertical stress difference or bedding plane cohesion weakens the promoting effect of thermal stress on bedding plane activation. The findings of this study provide a theoretical basis for forecasting fracture propagation morphology in field operations targeting deep shale reservoirs.