In the Standard Model of gaseous stars, temperature plays an indispensable role in generating the gas pressure which prevents ‘gravitational collapse’. Yet, as stars age in this model, changes in thermonuclear fuel lead to decreased temperatures and associated internal pressures. Gravitational forces between gas particles begin to dominate and stellar collapse results. The process results in ultra-dense compact objects including white dwarfs, neutron stars, and black holes. The Chandrasekhar limit plays a central role in the theory of white dwarfs by constraining dwarf mass. These transformations have been described using thermodynamic expressions. Yet, within any given thermodynamic relation, not only must units balance on each side, but so too must thermodynamic character. Whether or not equilibrium conditions are established, temperature must always be intensive in macroscopic thermodynamics and mass must always be extensive. The theory of temperatures and pressures within gaseous stars is constructed from the kinetic theory of an ideal gas, by which temperature is introduced, in combination with gravitational and Coulomb forces. The resulting thermodynamic relations impart non-intensive character to temperature, non-extensive character to mass, and thermodynamically unbalanced luminosity relations. Consequently, the theory of gravitational collapse of gaseous stars to form compact stellar objects is not valid. Stars cannot be gaseous in nature. Rather, they must be comprised of condensed matter, most likely metallic hydrogen, and therefore essentially incompressible.