by Garrison W. Bullard, Lauren B. Buckley, Joel G. Kingsolver Predicting survival of ectotherms in stressful and variable thermal environments is an essential challenge in this era of heat waves and climate change. Recent thermal death time (TDT) models, based on an exponential relationship between average time to death (or failure) t f and temperature, enable accounting for average survival responses to both the magnitude and duration of stressful temperatures. However, extending these deterministic and probabilistic models to predict patterns of survival in fluctuating temperatures currently requires additional assumptions: e.g., that injury accumulation due to heat stress is additive across temperatures, and that the shape of the cumulative survival curve does not change with temperature. We evaluate these assumptions and their consequences by using a parametric survival model and available data on failure (knockdown) times of adult Drosophila. We find that the variance in log( t f