  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
$\mathfrak{a} \rho^2 (\rho \mathfrak{a}^3)^{1/2}$.
