We study the heat capacity of isolated giant vortex states, which are good an-gular momentum (L) states, in a mesoscopic superconducting disk using the Ginzburg-Landau (GL) theory. At small magnetic fields the L = 0 state qualitatively behaves like the bulk sample characterized by a discontinuity in heat capacity at Tc. As the field is increased the discontinuity slowly turns into a continuous change which is a finite-size effect. The higher L states show a continuous change in heat capacity at Tc at all fields. We also show that for these higher L states, the behavior of the peak position with change in field is related to the paramagnetic Meissner effect (irreversible) and can lead to an unambiguous observation of positive magnetization in mesoscopic superconductors.