  We report the specific heat $c_N$ around the melting transition(s) of
micrometer-sized superparamagnetic particles confined in two dimensions,
calculated from fluctuations of positions and internal energy, and
corresponding Monte Carlo simulations. Since colloidal systems provide single
particle resolution, they offer the unique possibility to compare the
experimental temperatures of peak position of $c_N(T)$ and symmetry breaking,
respectively. While order parameter correlation functions confirm the
Kosterlitz-Thouless-Halperin-Nelson-Young melting scenario where translational
and orientational order symmetries are broken at different temperatures with an
intermediate so called hexatic phase, we observe a single peak of the specific
heat within the hexatic phase, with excellent agreement between experiment and
simulation. Thus, the peak is not associated with broken symmetries but can be
explained with the total defect density, which correlates with the maximum
increase of isolated dislocations. The absence of a latent heat strongly
supports the continuous character of both transitions.
