In ectotherms, the performance of physiological, ecological and life-history traits universally increases with temperature to a maximum before decreasing again. Identifying the most appropriate thermal performance model for a specific trait type has broad applications, from metabolic modelling at the cellular level to forecasting the effects of climate change on population, ecosystem and disease transmission dynamics. To date, numerous mathematical models have been designed, but a thorough comparison among them is lacking. In particular, we do not know if certain models consistently outperform others and how factors such as sampling resolution and trait or organismal identity influence model performance. To fill this knowledge gap, we compile 2,739 thermal performance datasets from diverse traits and taxa, to which we fit a comprehensive set of 83 existing mathematical models. We detect remarkable variation in model performance that is not primarily driven by sampling resolution, trait type, or taxonomic information. Our results reveal a surprising lack of well-defined scenarios in which certain models are more appropriate than others. To aid researchers in selecting the appropriate set of models for any given dataset or research objective, we derive a classification of the 83 models based on the average similarity of their fits.