An a.c. calorimetric heat capacity measurement has been performed on high-quality synthetic quartz,It was found that at the incommensurate (IC)-beta-phase transition, the heat capacity C-p of as-grown samples show critical behavior, i.e. there is a sharp peak at the IC-beta transition. The shapes of the C-p are almost identical in both heating and cooling runs. However, when as-grown samples were annealed in the alpha-phase just below the alpha-IC transition, the C-p peak became considerably rounded and, at the same time, the transition temperature slightly increased, The shapes of the C-p peaks on heating and cooling became dissimilar for the annealed samples.