High temperature heat capacity data of the same solid reported by different authors can differ from each other by much more than can reasonably be attributed to the experimental errors, and seem to have a systematic origin. In this communication it will be shown that each individual data set can adequately be described by a “critical” power function of type ~(Tm-T)α plus an absolute constant (Tm=melting temperature). Commonly the critical power function holds for all heat capacity data of larger than atomistic Dulong-Petit (D-P) limit. Within the large critical range crossover phenomena between different power functions with different exponents α can additionally occur. For the asymptotic power functions (T→Tm) exponents near to the rational numbers of α=2/3, 1 and 1.5 are identified. For the non asymptotic power functions the identified exponents are α=0 (logarithmic divergence), 1/3, 1/2 and 2. Quite generally, a large validity range of the critical power function indicates that the heat capacity is not of atomistic origin but has to be attributed to a field of freely propagating bosons. This view is in analogy to the main issue of RG theory that the dynamics in the vicinity of the magnetic ordering transition is not due to exchange interactions between spins but due to a boson guiding field. The postulated bosons at melting transition are not specified as yet but they are evidently excitations of the continuous solid with energies of much larger than the atomistic excitations (phonons). The floating heat capacity near Tm can be explained by a mean free path of the bosons that is of the order of the linear dimension of the sample. The heat capacity of the field then depends on size, shape and surface quality of the sample. It therefore appears not possible to define an intrinsic behavior.