We investigate the accuracy of the expression of Rosenfeld and Tarazona (RT) for the excess isochoric heat capacity, C(V)(ex)∝T(-2/5), for 18 model liquids. Previous investigations have reported no unifying features of breakdown for the RT expression. Here, liquids with different stoichiometric composition, molecular topology, chemical interactions, degree of undercooling, and environment are investigated. The RT expression is a better approximation for liquids with strong correlations between equilibrium fluctuations of virial and potential energy, i.e., "Roskilde-simple" liquids [T. S. Ingebrigtsen, T. B. Schrøder, and J. C. Dyre, Phys. Rev. X 2, 011011 (2012)]. This observation holds even for molecular liquids under severe nanoscale confinement which does not follow from the original RT bulk hard-sphere fluid perturbation theory arguments. The density dependence of the specific heat is predicted from the isomorph theory for Roskilde-simple liquids, which in combination with the RT expression provides a complete description of the specific heat's density and temperature dependence.