To obtain satisfied results with a high precision in the thermal stress analysis simulating construction process of mass concrete structures by using FEM, the refined finite element mesh is necessary and thus much computation is required. Being convenient in adaptive analysis and in mesh division, the numerical manifold method (NMM) is introduced to compute thermal field and thermal stresses and the formulae based on high-order NMM are derived. According to the derived formulae, in which all integrands are only the product of polynomial bases and convenient for implementation of the simplex integration, a program is developed and verified by examples, providing a new approach for the thermal stress analysis of mass concrete structures. Examples show that the NMM can rapidly improve the results by raising the order of cover function on a coarse mesh.