Considerable uncertainty remains about the combined effects of multiple limiting factors on oceanic phytoplankton, which constitute the base of the marine food web and mediate biogeochemical cycles of carbon and nutrients. I apply Bayesian statistical analysis to disentangle the combined effects of temperature and concentration on uptake of the important nutrient nitrate as measured by oceanic field experiments. This provides consistent estimates of temperature sensitivities for the maximum uptake rate and affinity (initial slope), the two parameters which define the shape of the uptake-concentration curve. No evidence is found that the temperature sensitivities of these two parameters differ, which implies that half-saturation constants, as commonly obtained by fits of the Michaelis-Menten (MM) equation, should be independent of temperature. This explains the robust relationship between half-saturation values and ambient nitrate concentration observed in compilations of data from diverse studies of uptake in marine and freshwater environments. Compared to the MM kinetics as applied in most large-scale models, accounting for a physiological trade-off between maximum uptake rate and affinity: (1) yields a more consistent model, which better describes observed changes in the shape of the uptake-concentration curve, and (2) implies a significantly greater inferred temperature sensitivity for nitrate uptake. These findings impact our understanding of how marine ecosystems and biogeochemical cycles will respond to climate change and anthropogenic nutrient inputs, both of which are expected to alter the relationship between nutrient concentrations and temperature in the near-surface ocean.