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A direct method is developed to estimate the boundary condition in two-dimensional inverse heat conduction problems. At the beginning of the study, finite-difference methods are employed to discretize the problem domain and then a linear inverse model is constructed to identify the boundary condition. The linear least-squares method is adopted for the linear model and thus iteration times can be limited to one cycle and the uniqueness of the solutions can be identified easily. Results from the examples confirm that the proposed method is effective and applicable to solution of multidimensional inverse heat conduction problems. In the example problems, three kinds of measuring methods are adopted to estimate the surface temperature. The result shows that only a few measuring points is sufficient to estimate the surface temperature when the measurement errors are neglected. When the measurement errors are considered, more measuring points are needed in order to increase the congruence of the estimated results to the exact solutions.