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To evaluate the high temperature sensing properties of metal oxide and perovskite materials suitable for use in combustion environments, it is necessary to understand the temperature dependence of their bandgaps. Although such temperature-driven changes can be calculated via the Allen–Heine–Cardona (AHC) theory, which assesses electron–phonon coupling for the bandgap correction at given temperatures, this approach is computationally demanding. Another approach to predict bandgap temperature-dependence is the O’Donnell model, which uses analytical expressions with multiple fitting parameters that require bandgap information at 0 K. This work employs data-driven Gaussian process regression (GPR) to predict the parameters employed in the O’Donnell model from a set of physical features. We use a sample of 54 metal oxides for which density functional theory has been performed to calculate the bandgap at 0 K, and the AHC calculations have been carried out to determine the shift in the bandgap at non-zero temperatures. As the AHC calculations are impractical for high-throughput screening of materials, the developed GPR model attempts to alleviate this issue by predicting the O'Donnell parameters purely from physical features. To mitigate the reliability issues arising from the very small size of the dataset, we apply a Bayesian technique to improve the generalizability of the data-driven models as well as quantify the uncertainty associated with the predictions. The method captures well the overall trend of the O’Donnell parameters with respect to a reduced feature set obtained by transforming the available physical features. Quantifying the associated uncertainty helps us understand the reliability of the predictions of the O’Donnell parameters and, therefore, the bandgap as a function of temperature for any novel material.