We have conducted heat-capacity measurements near the smectic-A - smectic-C* phase transition in free-standing films of a chiral liquid-crystal compound. The heat-capacity behavior confirms the evolution of the transition in the interior layers from first to second order as a function of film thickness suggested earlier in tilt angle measurements. The asymmetry in the heat-capacity anomaly exhibits an interesting crossover in thinner films. We also observed the phase transitions leading to the crystallization to the tilted crystal-G in these films at lower temperatures. The surface ordering strength in these films is found to be much larger than that in other smectic films, which we speculate is due to the molecular tilt.