Thousands of studies estimate climate change impacts related to temperature, but temperature is rarely measured at the exact location where impacts occur. Empirical work uses proxies such as closest station readings or estimates from gridded data products like PRISM. Measurement error introduced from this practice is routinely ignored. When acknowledged, it is typically assumed small in magnitude and classically (i.i.d. normal) distributed, implying that impact estimates are modestly attenuated toward zero. This assumption is formally examined by treating temperature readings at US weather stations as ground truth, then predicting daily mean temperature there using various proxies. This allows precise identification of measurement errors in an otherwise error-free relationship. The results contradict the standard assumption. These errors exhibit strong spatial and temporal components and, often, are large in magnitude. While proxy measurement errors typically cause downward bias, overestimates are common. Estimation problems are concentrated where attention focuses—the temperature distribution’s tails.