An apparatus for measuring the filling level in a liquid vessel, in particular in a reactor vessel of a nuclear-engineering plant, with a plurality of elongate, spaced-apart measurement tubes. Each measurement tube has a number of thermocouples which are distributed in the longitudinal direction. A thermocouple, which acts as a primary signal transmitter, is heated by a heating element and is arranged on a first measurement tube, has assigned to it on the signal side an unheated thermocouple, which acts as a reference signal transmitter and is arranged on a measurement tube which is different from the first measurement tube.