We performed a theoretical study of the specific heat, as a function of the temperature, for double-strand DNA quasiperiodic sequences. The energy spectra are calculated using the 2-D Schrödinger equation, in a tight-binding approximation, with the on-site energy exhibiting long-range disorder and nonrandom hopping amplitudes. Classical, quantum, and nonextensive statistics are taken into account to perform the specific heat spectra. Comparisons are made with finite segment of natural DNA, as part of the human chromosome Ch22. Furthermore, we consider the effects of the solvent interaction on the nonlinear dynamical structure of a DNA segment, by using a time-independent perturbation approach, to investigate the denaturation temperature profiles of some DNA’s thermodynamic functions, such as the stretching of the hydrogen bonds, the specific heat, and the entropy. Besides a sharp thermal profile behavior of these functions, we also observe that the DNA’s melting temperature decreases as the solvent potential increases.