Over the last few decades, biologists have made substantial progress in understanding relationships between changing climates and organism performance. Much of this work has focused on temperature because it is the best kept of climatic records, in many locations it is predicted to keep rising into the future, and it has profound effects on the physiology, performance, and ecology of organisms, especially ectothermic organisms which make up the vast majority of life on Earth. Nevertheless, much of the existing literature on temperature-organism interactions relies on mean temperatures. In reality, most organisms do not directly experience mean temperatures; rather, they experience variation in temperature over many time scales, from seconds to years. We propose to shift the focus more directly on patterns of temperature variation, rather than on means per se, and present a framework both for analyzing temporal patterns of temperature variation and for incorporating those patterns into predictions about organismal biology. In particular, we advocate using the Fourier transform to decompose temperature time series into their component sinusoids, thus allowing transformations between the time and frequency domains. This approach provides (1) standardized ways of visualizing the contributions that different frequencies make to total temporal variation; (2) the ability to assess how patterns of temperature variation have changed over the past half century and may change into the future; and (3) clear approaches to manipulating temporal time series to ask "what if" questions about the potential effects of future climates. We first summarize global patterns of change in temperature variation over the past 40 years; we find meaningful changes in variation at the half day to yearly times scales. We then demonstrate the utility of the Fourier framework by exploring how power added to different frequencies alters the overall incidence of long-term waves of high and low temperatures, and find that power added to the lowest frequencies greatly increases the probability of long-term heat and cold waves. Finally, we review what is known about the time scales over which organismal thermal performance curves change in response to variation in the thermal environment. We conclude that integrating information characterizing both the frequency spectra of temperature time series and the time scales of resulting physiological change offers a powerful new avenue for relating climate, and climate change, to the future performance of ectothermic organisms.