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A computational paradigm for solving one-dimensional transient heat transfer problems is presented. The basic parameters in the paradigm are the lowest and highest eigenvalues for the system of differential equations and the number of time steps to steady state. The paradigm includes equations for an a priori time step value for the single step methods. A new sampling procedure was used with the numerical experimentation as well as a new decision criterion for accepting a time step value. The paradigm was validated by calculating an error norm for nine heat transfer problems. The paradigm provides time step values that give accurate values for the four single step methods in Cartesian, radial, and spherical one-dimensional problems. The computational procedure is limited to heating and cooling problems that go to equilibrium.