Alluvial systems may respond to climatic fluctuations in a variety of ways. These responses include adjustments in: (1) channel dimensions, (2) grain size, (3) channel mobility, (4) planform morphology, and (5) slope. While on the reach-scale these adjustments may be rapid, it is not entirely clear how they are propagated within the entire system in concert with the climatic change. A more quantitative framework and understanding would be beneficial for predicting basin-scale stratigraphic shifts. Further complicating our understanding of climatic impacts on alluvial stratigraphy are various autogenic processes that dampen, mute, and shred climatic variability as well as the inherent stochastic variation within even a steady state river system. Addressing these issues and responses requires quantitative, independent constraints on both the paleoclimate and fluvial deposits. Herein, I present several metrics of fluvial systems spanning a known interval of abrupt and dramatic global warming, the Paleocene-Eocene Thermal Maximum (PETM). The magnitude, timing, and duration of the PETM can be compared independently to the fluvial response using geochemical proxies. In each of the three basins examined (Bighorn Basin, Wyoming, USA; Piceance Basin, Colorado, USA; Tremp-Graus Basin, Pyrenees, Spain) a coarse-grained pulse of sediment correlates with the carbon isotope excursion demarking the PETM. These observations are broadly consistent with existing 2-D numerical models of basin-fill subject to a change in discharge. However, the timing of the pulse differs in each basin as well as the details of channel dimensions, lithofacies, grain size, and sand-body geometries. However, all three exceed background autogenic variability estimates. The differences in timing of the coarse-grained pulse of sediment and inferred unconformities are consistent with those expected from 2-D diffusional models that take into account the basin equilibrium timescale and catchment size relative to the rate of discharge (i.e., climate) change. These changes are also reflected in the channel-stacking density, with differences in lithofacies, channel dimensions, and overbank deposition amongst the three study areas suggesting different mechanisms by which the geomorphic system is mediating the climatic change.