Extrinsic environmental factors influence the distribution and population dynamics of many organisms, including insects that are of concern for human health and agriculture. This is particularly true for vector-borne infectious diseases like malaria, which is a major source of morbidity and mortality in humans. Understanding the mechanistic links between environment and population processes for these diseases is key to predicting the consequences of climate change on transmission and for developing effective interventions. An important measure of the intensity of disease transmission is the reproductive number R0. However, understanding the mechanisms linking R0 and temperature, an environmental factor driving disease risk, can be challenging because the data available for parameterization are often poor. To address this, we show how a Bayesian approach can help identify critical uncertainties in components of R0 and how this uncertainty is propagated into the estimate of R0. Most notably, we find that different parameters dominate the uncertainty at different temperature regimes: bite rate from 15 degrees C to 25 degrees C; fecundity across all temperatures, but especially approximately 25-32 degrees C; mortality from 20 degrees C to 30 degrees C; parasite development rate at degrees 15-16 degrees C and again at approximately 33-35 degrees C. Focusing empirical studies on these parameters and corresponding temperature ranges would be the most efficient way to improve estimates of R0. While we focus on malaria, our methods apply to improving process-based models more generally, including epidemiological, physiological niche, and species distribution models.