A model based feedback control algorithm is developed for parabolic type distributed parameter systems in two-dimensional space. The model used is a fully decoupled state space model which is obtained by applying the finite integral transform technique to the phenomenological model of a process. A state feedback controller is designed for the state space model by using a Kalman filter as an observer. The proposed method is applied to control of temperature distribution in a two dimensional heat conduction process. It is demonstrated that the temperature distributions can be accurately estimated by use of a small number of sensors and controlled satisfactorily even when some model error exists.