Due to the use of two cover systems, i.e., the mathematical cover system and the physical cover system, the numerical manifold method (NMM) is able to solve both continuous and discontinuous problems within the same framework. In the present paper, the NMM is developed to analyze unsteady heat conduction problems in two-dimensional settings. The NMM discrete equations are derived using the weighted residual method in Galerkin form. The spatial integration is performed through triangulation and Gauss quadrature while time integration is realized by the backward Euler scheme. The proposed approach is verified through a typical numerical example.