One challenge for statisticians and epidemiologists in projecting the future health risks of climate change is how to estimate exposure-response relationships when temperatures are higher than at present. Low dose extrapolation has been an area of rich study, resulting in well-defined methods and best practices. A primary difference between high dose and low dose extrapolation of exposure-response relationships is that low dose extrapolation is bounded at no exposure and no (or a baseline) response. With climate change altering weather variables and their variability beyond historical values, the highest future exposures in a region are projected to be higher than current experience. Modelers of the health risks of high temperatures are making assumptions about human responses associated with exposures outside the range of their data; these assumptions significantly affect the magnitude of projected future risks. Further, projections are affected by adaptation assumptions; we explore no adaptation (extrapolated response); individual (physiological) adaptation; and community adaptation. We present an example suggesting that linear models can make poor predictions of observations when no adaptation is assumed. Assumptions of the effects of weather above what has been observed needs to be more transparent in future studies. Statistical simulation studies could guide public health researchers in identifying best practices and reducing bias in projecting risks associated with extreme temperatures. Epidemiological studies should evaluate the extent and time required for adaptation, as well as the benefits of public health interventions.