Studies of climate change impacts on the weather have often focused on summary statistics of mean, variance and extremes (e.g., max, min, 95th percentile). However, recent epidemiological studies suggested that rapid, abrupt and extreme day-to-day changes in temperature are strongly linked to higher hospitalization and mortality rates, and they have significant impact on human health. Motivated by these findings, we present in this study an in-depth, statistical analysis of day-to-day temperature fluctuations in the contiguous United States for the period 1950 - 2019. We use both observations and reanalysis datasets to examine the spatial patterns, seasonality and long-term trends in the magnitude of extreme day-to-day temperature fluctuations. Our results show that most stations in Central and Eastern United States exhibit an increasing trend of 0.2 - 0.3 C/decade in the magnitude of extreme temperature fluctuations. We also show that reanalysis datasets while capturing the spatial variability of rapid temperature fluctuations, they underestimate the magnitudes and fail to reproduce observed trends. This discrepancy is attributed to inadequate representation of processes that leads to rapid changes in temperature in numerical weather prediction (NWP) models. Overall, we argue that studies of climate change impacts on the weather should go beyond classical summary statistics to examine rapid changes in variables such as temperature due to their significant socioeconomic impacts.