As machine learning models continue to grow more complex, poor calibration significantly limits the reliability of their predictions. Temperature scaling learns a single temperature parameter to scale the output logits, and despite its simplicity, remains one of the most effective post-hoc recalibration methods. We identify one of temperature scaling's defining attributes, that it increases the uncertainty of the predictions in a manner that we term homogenization, and propose to learn the optimal recalibration mapping from a larger class of functions that satisfies this property. We demonstrate the advantage of our method over temperature scaling in both calibration and out-of-distribution detection. Additionally, we extend our methodology and experimental evaluation to recalibration in the Bayesian setting.