We propose a cooling mechanism for ultracold fermionic atom ensembles, which capitalizes on the energy dependence of inelastic collisions near a Feshbach resonance. We first discuss a single magnetic resonance and find that the final temperature and cooling rate is limited by the resonance width. A concrete example for a p-wave resonance of K-40 is given. We then improve upon this setup by using both a sharp optical or radio-frequency-induced resonance and a broad magnetic resonance and show that one can improve upon temperatures reached with current technologies.