The thermal history of arthropod predators and their prey may affect their reproductive performance during heat waves. Thus, a matching juvenile and adult environment should be beneficial as it enables the individuals to acclimate to extreme conditions. Prey fecundity, however, is also affected by a second stressor, namely predation risk. Here, we assessed the impact of extreme and mild heat waves on the reproductive output of acclimated (juvenile and adult heat wave conditions are matching) and non-acclimated females of the biocontrol agent Phytoseiulus persimilis, a predatory mite, and its herbivorous prey, the two-spotted spider mite Tetranychus urticae, on bean leaves. Their escape and oviposition rates and egg sizes were recorded over 10 days. Additionally, ovipositing prey females were exposed to predator cues and heat waves. Acclimation changed the escape rates and egg sizes of both species, whereas fecundity was only influenced by the adult thermal environment via increased egg numbers under extreme heat waves. Acclimation reduced predator and prey escape rates, which were higher for the predator. Pooled over acclimation, both species deposited more but smaller eggs under extreme heat waves. Acclimation dampened this effect in prey eggs, whereas acclimation resulted in smaller female eggs of the predator. Prey deposited larger male and female eggs. Predator cues reduced prey oviposition, but the effect was small compared to the large increase gained under extreme heat waves. We argue that the success of predators in controlling spider mites during heat waves mainly depends on the fates of escaping predators. A permanent absence of predators may result in the numerical dominance of prey.