We review results of a high resolution systematic study of the specific heat for alkyl-cyanobiphenyl liquid crystals confined to the 0.2µm diameter cylindrical pores Anopore membranes. The nematic director alignment at the pore wall is varied from homeotropic to tangential by pore surface treatment. Several phenomena are uncovered by these studies which probed the weakly first order nematic to isotropic, the continuous smectic-A to nematic and the first order smectic-A to isotropic phase transitions. The specific heat is strongly dependent on the nematic director configuration, and confinement effects are remarkably distinct according to the order of the phase transition. The influence of elastic distortions and surface ordering and disordering effects are evident. Despite considerable departures from bulk behavior with regards to specific heat peaks size, rounding and width, and transition temperature shifts, a bulk-like critical behavior appears to be retained. The formation of smectic translational order within the pores is hindered for those liquid crystals that also possess a nematic phase. The average scalar order parameter temperature dependence is extracted from the specific heat results using a simplified Landau-de Gennes type of model, and is shown to be consistent with nuclear magnetic resonance results.