Abstract: A numerical manifold method (NMM) for 2-dimentional unsteady temperature field of fractured rock mass is proposed based on NMM for triangle finite covers. Furthermore, the penalty method for the first temperature boundary condition is proposed and calculating format is provided. NMM has two kinds of covers, namely mathematical cover and physical cover. The mathematical cover is independent of the physical domain of the problem, and its generation will not consider the number, position and orientation of the fractures, which can avoid the inconvenience of mesh generation on fractured areas. The two sides of the fracture have different manifold elements, and as a result, temperature discontinuity across the crack surface is achieved. Considering the fractures as the internal manifold elements or boundary conditions, which will affect the global governing equations lastly, the temperature field of fractured rock mass can therefore be solved by using NMM. The proposed method is featured in high accuracy and has the possibility of solving the temperature problem of fractured rock mass which contains arbitrary discontinuous segments. Finally, the examples from literatures show that the results are consistent with those of the general methods.