We consider the following model: the temperature $z(t,x)$ evolves on a bounded $x$-interval and we are allowed to choose a pointwise control (e.g. one prescribes the temperature at the left end). The classical problem of control theory is the exact controllability: given a horizon time $T$ and a final state $z^T(x)$, find a control such that the solution satisfies $z(T,x) = z^T(x)$ for all $x$. This question has now a definitive solution, which I will recall. We will then consider the (different) problem of output tracking, for which one defines an output $y(t)$ measured from the state $z(t)$ (e.g. a point measurement $y(t) = z(t,x_0)$). Given a reference signal $y_ref(t)$, the objective is to find a control such that $y(t) = y_ref(t)$ for all $t$. When the output is a point measurement, we are able to completely characterize these trackable signals, in collaboration with P. Lissy (CERMICS). I will sketch the proof of this result, which relies on Paley-Wiener theory and a new Plancherel type isometry for Gevrey functions. If the time permits I will also present a consequence of our result, which connects Gevrey-2 functions with the Bergman space over a square.