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We explore thermodynamics of an ideal gas system with heat conduction,incorporating a model that accommodates heat dependence. Our model isconstructed based on i) the first law of thermodynamics from action formulationand ii) the existence condition of a (local) Lorentz boost between an Eckartobserver and a Landau-Lifschitz observer--a condition that extends thestability criterion of thermal equilibrium. The implications of theseconditions include: 1) Heat contributes to the energy density through thecombination $q/n\Theta^2$ where $q$, $n$, and $\Theta$ represent heat, numberdensity, and temperature, respectively. 2) The energy density exhibits a uniqueminumum at $q=0$ with respect to the contribution. 3) Our findings indicate anupper bound on the temperature of the ideal gas in thermal equilibrium. Theupper bound is governed by the coefficient of the first non-vanishingcontribution of heat around equilibrium to the energy density.

Temperature upper bound of an ideal gas