We consider the real β-ensemble (or 1D log-gas) of dimension N in the high-temperature regime, i.e. where the inverse temperature β scales as Nβ = 2P, with P a fixed positive parameter. We establish the large-N asymptotic expansion at all orders of the partition function: (Formula Presented) for V (x) = x2 + φ(x) with φ a bounded smooth function, and identify the first two terms of this expansion. In this regime, the energy no longer dominates the entropy, as in the fixed-β case, but rather scales at the same order in N. Consequently, at large N, the system is macroscopically described by the so-called thermal equilibrium measure which is supported on the entire real line. Our proof relies on the loop equations method, previously applied in the fixed-β setting in [BG13b, BG13a], and provides the first example in which this approach can be successfully implemented using the thermal equilibrium measure. This requires a detailed understanding of both the thermal equilibrium measure and the associated master operator, an unbounded differential operator, leading to several new analytical challenges. In this setting, we carry out a technically involved analysis to obtain precise estimates for the inverse of the master operator in suitable functional norms. In addition we establish, through subtle operator arguments, a crucial continuity property of the equilibrium density with respect to the potential dependence. These two results constitute the main novelties of the paper and allow us to exhibit a new class of multiple integrals for which such an expansion can be obtained, while providing a deeper understanding of the thermal equilibrium measure and its properties. Asymptotics of the partition function for β-ensembles at high temperature.