  We consider the linear heat equation with a Wentzell-type boundary condition
and a Dirichlet control. Such a boundary condition can be reformulated as one
of dynamic type. First, we formulate the boundary controllability problem of
the system within the framework of boundary control systems, proving its
well-posedness. Then we reduce the question to a moment problem. Using the
spectral analysis of the associated Sturm-Liouville problem and the moment
method, we establish the null controllability of the system at any positive
time $T$. Finally, we approximate minimum energy controls by a penalized HUM
approach. This allows us to validate the theoretical controllability results
obtained by the moment method.
