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In this paper, we consider boundary control problems for a distributed heating system. The dynamical model of the heating system under consideration is given by a parabolic partial differential equation. This type of mathematical model is also a common description for other distributed parameter systems involving heat and mass transfer. After derivation of a suitable, general-purpose solution procedure for the design of flatness-based open-loop as well as closed-loop boundary control strategies, we present experimental results, which highlight the applicability in a real-world experiment. An alternative solution to the control problem is derived based on the method of integrodifferential relations. The quality of the flatness-based approximation is verified by comparison of the results of both design procedures. For the experimental validation, a test setup at the University of Rostock is used. It consists of a metallic rod equipped with a finite number of Peltier elements which are used as distributed control inputs allowing for active cooling and heating. To compensate unmodeled disturbances, closed-loop output feedback control strategies are extended by state and disturbance observers. [ABSTRACT FROM AUTHOR]