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For strongly dissipative H\'enon maps at the first bifurcation where theuniform hyperbolicity is destroyed by the formation of tangencies inside thelimit set, we establish a thermodynamic formalism, i.e., prove the existenceand uniqueness of an invariant probability measure which maximizes the freeenergy associated with a non continuous geometric potential $-t\log J^u$, where$t\in\mathbb R$ is in a certain large interval and $J^u$ is the Jacobian in theunstable direction. We obtain geometric and statistical properties of thesemeasures.

Equilibrium measures for the H\'enon map at the first bifurcation: uniqueness and geometric/statistical properties