  The Berezinskii-Kosterlitz-Thouless (BKT) transition is expected to have a
clear signature on the specific heat. The singularity at the transition
temperature $T_{BKT}$ is predicted to be immeasurable, and a broad
non-universal peak is expected at $T>T_{BKT}$. Up to date this has not been
observed in two-dimensional superconductors. We use a unique highly sensitive
technique to measure the specific heat of ultrathin Pb films. We find that
thick films exhibit a specific heat jump at $T_C$ that is consistent with BCS
theory. As the film thickness is reduced below the superconducting coherence
length and the systems enters the 2D limit the specific heat reveals BKT-like
behavior. We discuss these observations in the framework of the continuous
BCS-BKT crossover as a function of film thickness.
