A general method of solution using the boundary element method (BEM) is developed for multi dimensional inverse problems of heat conduction. A concrete formulation is presented for the one-dimensional problem in which the surface temperature and the surface heat flux are sought from the temperature measured at two interior points. By solving the Beck's problem, the stability of the calculation is studied, and the result is compared with that of the method based on the Duhamel theorem. A simple two-dimensional problem is also dealt with in an attempt to show the applicability of the present method.