Many quality problems in continuous-cast steel are related to mold level fluctuations, stickers, deep oscillation marks, and other events at the meniscus. These phenomena may be detected by monitoring temperature signals in the wall of the copper mold. This work applies computational models of transient heat conduction to investigate the potential capabilities of mold thermocouples to detect such phenomena by computing the sensitivity of the detected signal to heat flux variations at the meniscus. The three-dimensional model is first validated with temperature data recorded in a commercial slab casting mold, and in a previous laboratory measurement. The method is capable of monitoring meniscus level, and to detect large surface level fluctuations. However, its ability to detect temperature fluctuations decreases with decreasing magnitude and duration of the level fluctuations and the distance of the thermocouple from the hot-face surface. Sensitivity calculations with the model are presented to quantify these detection limits. Finally, a new inverse heat-conduction model is applied to extract new insights into heat transfer at the meniscus from thermocouple measurements.