Climate change is affecting biodiversity and ecosystem function worldwide, and the lowland tropics are of special concern because organisms living in this region experience temperatures that are close to their upper thermal limits. However, it remains unclear how and whether tropical lowland species will be able to cope with the predicted pace of climate warming. Additionally, there is growing interest in examining how quickly thermal physiological traits have evolved across taxa, and whether thermal physiological traits are evolutionarily conserved or labile. We measured critical thermal maximum (CTmax) and minimum (CTmin) in 56 species of lowland Amazonian frogs to determine the extent of phylogenetic conservatism in tolerance to heat and cold, and to predict species' vulnerability to climate change. The species we studied live in sympatry and represent ~65% of the known alpha diversity at our study site. Given that critical thermal limits may have evolved differently in response to different temperature constraints, we tested whether CTmax and CTmin exhibit different rates of evolutionary change. Measuring both critical thermal traits allowed us to estimate species' thermal breadth and infer their potential to respond to abrupt changes in temperature (warming and cooling). Additionally, we assessed the contribution of life history traits and found that both critical thermal traits were correlated with species' body size and microhabitat use. Specifically, small direct-developing frogs in the Strabomantidae family appear to be at highest risk of thermal stress while tree frogs (Hylidae) and narrow mouthed frogs (Microhylidae) tolerate higher temperatures. While CTmax and CTmin had considerable variation within and among families, both critical thermal traits exhibited similar rates of evolutionary change. Our results suggest that 4% of lowland rainforest frogs assessed will experience temperatures exceeding their CTmax, 25% might be moderately affected and 70% are unlikely to experience pronounced heat stress under a hypothetical 3°C temperature increase.