There is increasing concern that the effects of biological invasions may be magnified by other human-induced global changes. Here, we compare the non-consumptive effects imposed by invasive vs. native predators and how these (differential) responses to both predator types depend on warming and prey latitude. We raised damselfly larvae from central- and high-latitudes in incubators under two temperatures (current [20 °C] and warming [24 °C]) and further exposed them to one of three predator cues: noble (native), signal (invasive at both latitudes) and spiny-cheek (invasive at central- but absent at high latitudes) crayfish. Growth rate increased in central-latitude but decreased in high-latitude prey in response to both noble and signal crayfish. The spiny-cheek crayfish only reduced growth rate in high-latitude prey. Cues from all three crayfish species generally caused a higher net energy budget, but only under warming. Our results demonstrated that high-latitude prey were able to recognize a novel invasive predator (spiny-cheek crayfish) cue, and revealed differential growth responses of central- and high-latitude prey toward the shared invasive predator (signal crayfish). Our data provide rare support for the concern that global change factors may magnify the impact of both native and novel invasive predators.