Based on a quantum modeling of the electronic transport, this work shows that ultra-thin solar cells can exhibit an improved open-circuit voltage VOC, without current reduction. This improvement is obtained when an energy-selective contact is considered between the absorber and the reservoir, and is attributed to a hot-carrier effect. While extraction with a nonselective contact does not generate hot carriers, the use of energy-selective contact induces an increase of carrier temperature up to 130 K and a corresponding VOC enhancement of 41 meV, considering an (In,Ga)As absorber. This enhancement agrees with a simple and general expression formulated in the quantum thermal machine field. Concerning the current, we show that current through an energy-selective contact is of the same order of magnitude as the one obtained without selectivity. This remarkable behavior, which is explained by the hybridization of states in the absorber with the state of the contact, requires a quantum confinement and thus an ultrathin absorber. Finally, we propose a simple rate model enabling an intuitive interpretation of the numerical results.