Abstract: Boundary control of a class of heat transfer distributed parameter systems is studied by the symmetry of differential equations and relationsship between symmetry and infinitesimal generator for satisfying different control objectives. The boundary control laws are designed to realize constant heating rate control at fixed point, steady state temperature control at fixed point, and boundary steady state temperature control for the heat transfer distributed parameter systems. The simulations for the controlled heat transfer distributed parameter system are illustrated the effectiveness of the control laws for the different control objectives.