This paper presents a technique for designing an approximately optimal feedback controller in a distributed parameter system. The problem investigated is a one-dimensional heat conduction system, The controller is designed by minimizing the difference in the performance measures between the one obtained for the optimal open loop control and the one obtained for the approximately optimal feedback control. The optimal open loop control is computed by means of the simplex method of linear programming. An approximately optimal feedback controller is designed using a gradient technique in the parameter sSpace to determine the best parameters and a search technique to determine the best spatial coordinates of the controller. The effect of the boundary conditions on the best parameters is discussed.