We consider a Bose gas at density \rho > 0, interacting through a repulsive potential V \in L^2 (\mathbb{R}^3) with scattering length \mathfrak{a} > 0. We prove an upper bound for the free energy of the system, valid at low temperature T \lesssim \rho \mathfrak{a}. Combined with the recent lower bound obtained in \cite{HabHaiNamSeiTri-23}, our estimate resolves the free energy per unit volume up to and including the Lee--Huang--Yang order \mathfrak{a} \rho^2 (\rho \mathfrak{a}^3)^{1/2}.
