The boundary face method (BFM), combined with a fast algorithm, was applied to transient heat conduction analysis of concrete dams during the pouring process, so as to predict the temperature distribution and its time history in concrete dams during the construction process. Using the time convolution method to compute the time integration and the Taylor series expansion method to separate the spatial variables and time variables in fundamental solutions, the spatial variable integrals can be calculated and stored at the same time, improving the calculation efficiency of the convolution integral. A case study shows that the temperature distribution obtained by the fast BFM agrees with the results of the finite element method, demonstrating the feasibility of application of the fast BFM to transient heat conduction analysis during the actual dam construction process.