A vertical column of an inviscid fluid, heated uniformly from below through a horizontal rigid bottom, is studied, with focus on the dynamics of the vapour/liquid interface near the three-phase (contact) line. The interfacial motion is induced by the competing effects of liquid feeding from above and evaporative mass loss through the interface. A linearized solution is obtained that describes the location of the contact line. The solution is used to study the transition processes to and from film boiling, where part of the liquid, lying on top of a vapour layer, can spontaneously be drawn downward and touch the heated bottom. Recession or advancement of the contact line then determines whether the film boiling is sustained or broken. It is seen that the correct contact-line dynamics cannot be predicted solely from a global mass balance in the liquid column.