The evolutionary potential of species to cope with short-term temperature fluctuations during reproduction is critical to predicting responses to future climate change. Despite this, vertebrate research has focused on reproduction under high or low temperatures in relatively stable temperate climates. Here, we characterize the genetic basis of reproductive thermal tolerance to temperature fluctuations in the ostrich, which lives in variable environments in tropical and subtropical Africa. Both heat and cold tolerance were under selection and heritable, indicating the potential for evolutionary responses to mean temperature change. However, we found evidence for a negative, genetic correlation between heat and cold tolerance that should limit the potential for adaptation to fluctuating temperatures. Genetic constraints between heat and cold tolerance appear a crucial, yet underappreciated, factor influencing responses to climate change.