A two-point boundary value problem for parabolic equations with a load term in a closed domain is considered. The loaded parabolic equation is reduced to a two-point boundary value problem for differential equations with a load term by discretizing the unknown function u(t, x) with respect to x using the method of lines. The resulting two-point boundary value problem is solved using the Dzhumabaev parameterization method. An algorithm for finding an approximate solution is proposed, and sufficient conditions for its convergence to a unique solution are obtained. The algorithm is implemented using well-known numerical methods. The feasibility and efficiency of the parameterization method make it possible to compute a numerical solution to the linear two-point boundary value problem with a load term. A test examples are provided to verify and demonstrate the proposed algorithm.