Since their discovery in 1822, supercritical fluids have been of enduring interest and have started to be deployed in many important applications. Theoretical understanding of the supercritical state is lacking and is seen to limit further industrial deployment. Here we study thermodynamic properties of the supercritical state and discover that specific heat shows a crossover between two different regimes, an unexpected result in view of currently perceived homogeneity of supercritical state in terms of physical properties. We subsequently formulate a theory of system thermodynamics above the crossover, and find good agreement between calculated and experimental specific heat with no free-fitting parameters. In this theory, energy and heat capacity are governed by the minimal length of the longitudinal mode in the system only, and do not explicitly depend on system-specific structure and interactions. We derive a power law and analyse supercritical scaling exponents in the system above the Frenkel line.