The evidence for the existence of the so-called linear thermal anomaly recently reported on the western margin of Mare Humorum is examined critically. Whether the anomalous cooling of Mare Humorum considered as a whole can be caused by internal heating is rejected on the basis of (1) the measured temperature differential compared to the environs observed during the lunar day, (2) the required temperature gradient, and (3) energy considerations compared to terrestrial heat flow. It is concluded that the observed hot spots are unlikely to be caused by internal heating.