<p>We consider a boundary control problem for a singularly perturbed parabolic equation with a linear time-periodic source having a solution in the form of a moving front. Our goal is to obtain a boundary condition that provides the required law of front motion. Based on the asymptotic analysis of the direct problem, we reduce the boundary control problem to solving algebraic equations connecting the asymptotic approximation of the front motion law with the coefficients in the equation and boundary conditions. We also provide a method for estimating the error that occurs when replacing the exact solution to a control problem with an asymptotic one.</p>