We study thermodynamical formalism for certain dissipative maps, that is maps with non-uniformly hyperbolic attractors, which are obtained from uniformly hyperbolic systems by the slow down procedure. Namely, starting with a hyperbolic local diffeomorphism $f : U \to M$ with an attractor $\Lambda$, one slows down trajectories in a small neighborhood of a hyperbolic fixed point $p \in \Lambda$ obtaining a nonuniformly hyperbolic diffeomorphism $g : U \to M$ with a topological attractor $\Lambda g$. We establish the existence of equilibrium measures for any continuous potential function on $\Lambda g$, however our main focus is the family of geometric $t$-potentials defined by $\varphi t(x) := -t \log|Df|_Eu(x)|$. We prove the existence of $t_0 < 0$ such that the equilibrium measures are unique for every $t \not= 1$ that belongs to the interval $(t_0,\infty)$. We also identify equilibrium measures for $t = 1$. Finally, we show that for $t \in (t_0,1)$ the equilibrium measures have exponential decay of correlations and satisfy the Central Limit Theorem.