Central temperature as a function of the central density for models with the same core mass and different carbon mass fractions X_C after core helium burning (indicated in the color bar). The previous evolution of the core (not shown here for clarity) is indistinguishable for all models, while the post-core-helium-burning evolution is greatly affected by the differences in central carbon abundance. Symbols indicate key evolutionary phases. To the right of the gray dashed line, electron degeneracy dominates the pressure. The inset axis indicates the final compactness of the models as a function of decreasing X_C.