  We study the dynamics of strongly dissipative H\'enon maps, at the first
bifurcation parameter where the uniform hyperbolicity is destroyed by the
formation of tangencies inside the limit set. We prove the existence of an
equilibrium measure which minimizes the free energy associated with the non
continuous potential $-t\log J^u$, where $t\in\mathbb R$ is in a certain
interval of the form $(-\infty,t_0)$, $t_0>1$ and $J^u$ denotes the Jacobian in
the unstable direction.
