Geological deposits can reveal how environments of the past have responded to climate change, enabling important insights into how environments may respond to our current anthropogenically induced warming. The Paleocene–Eocene Thermal Maximum (PETM) occurred ca. 56 Ma and was a short-lived (approximately 200,000 years) global warming event (5–8°C rise). The PETM has been investigated at several terrestrial and marine localities across the globe. However, many studies are based on single successions, with very few sites being placed within a well-defined spatial and temporal context and with comparisons limited to deposits that lie immediately above and below the event. Due to the inherent variability of sedimentary systems, it is imperative that the appropriate context is provided to fully understand the impacts of climate change on landscapes and subsequent deposits. This study examines 28 locations, totaling over 4 km of recorded stratigraphy, within a newly defined quantified sedimentary basin context (Bighorn Basin, USA) to evaluate variability of fluvial response to the PETM. We show that channel-body and story thicknesses across the PETM are not statistically significantly different from deposits outside the climate event, implying that there is not a consistent sedimentary response to the climate event across the basin. Based on our large dataset we calculate that precipitation would have had to double for statistically significant changes in deposit thickness to be generated. We discuss how climatic signals may be lost due to the self-organization, spatial–temporal varied response and preservation potential in large fluvial systems. This study gives a new quantified perspective to climate events in the geologic record.