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We provide a version of a thermodynamic formalism of entire transcendentalmaps that exhibit Baker domains, denoted as $f_{\ell, c}: \mathbb C\to \mathbbC$ and defined by $f_{\ell, c}(z)= c-(\ell-1)\log c+ \ell z- e^z$, where $\ell\in \mathbb N$, with $\ell \geq 2 $ and $c$ belongs to the disk $ D(\ell, 1)$in the complex plane. We show in particular the existence and uniqueness ofconformal measures and that the Hausdorff dimension is the unique zero of thepressure function $t\to P(t)$, for $t>1,$ where $J_r(f)$ is the radial Juliaset.

Thermodynamic formalism for entire transcendental maps with hyperbolic Baker Domains