  We prove a lower bound for the free energy (per unit volume) of the
two-dimensional Bose gas in the thermodynamic limit. We show that the free
energy at density $\rho$ and inverse temperature $\beta$ differs from the one
of the non-interacting system by the correction term $4 \pi \rho^2 |\ln a^2
\rho|^{-1} (2 - [1 - \beta_{\mathrm{c}}/\beta]_+^2)$. Here $a$ is the
scattering length of the interaction potential, $[\cdot]_+ = \max\{ 0, \cdot
\}$ and $\beta_{\mathrm{c}}$ is the inverse Berezinskii--Kosterlitz--Thouless
critical temperature for superfluidity. The result is valid in the dilute limit
$a^2\rho \ll 1$ and if $\beta \rho \gtrsim 1$.
