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Synopsis The fitness implications of climate variability and change are often estimated by integrating an organism’s thermal sensitivity of performance across a time series of experienced body temperatures. Although this approach is an important first step in evaluating an organism’s sensitivity to climate or climate change, it ignores potential influences of recent exposure to thermal stress on current thermal sensitivity. Here, we account for recent thermal stress by estimating rates of damage, repair, and other carryover effects; and we illustrate the approach with fecundity and development rate data from experiments that exposed aphids to various stressful and fluctuating temperatures. Our analyses indicate that heat stress for these aphids starts near the upper thermal limit for performance; that heat stress intensifies with both the exposure duration and with temperature; and that there is considerable capacity for repair at temperatures near the thermal optimum for performance. Results from experiments with aphids indicate that incorporating time series of damage, recovery, and repair will be necessary to anticipate fitness outcomes of climate change and variability.