A method is proposed for treating Stefan problems by solving two boundary value problems with moving sources whose strengths and positions become the unknowns. In the one (space) dimensional case three coupled nonlinear integral equations for the unknown source strengths and the position of the moving boundary are obtained by the use of fundamental solutions and the application of the boundary conditions on the moving boundary. It is shown that two known solutions satisfy the integral equations. The proposed method seems to be similar to one proposed in 1956 by \textit{I. I. Kolodner} [Commun. Pure Appl. Math. 9, 1-31 (1956; Zbl 0070.438)] in a paper cited in the present work. In the present work no analysis of the existence or uniqueness of solutions of the integral equations is given.