Prior work has shown that probability distributions of column water vapor and several passive tropospheric chemical tracers exhibit longer-than-Gaussian (approximately exponential) tails. The tracer-advection prototypes explaining the formation of these long-tailed distributions motivate exploration of observed surface temperature distributions for non-Gaussian tails. Stations with long records in various climate regimes in National Climatic Data Center Global Surface Summary of Day observations are used to examine tail characteristics for daily average, maximum and minimum surface temperature probability distributions. Each is examined for departures from a Gaussian fit to the core (here approximated as the portion of the distribution exceeding 30% of the maximum). While the core conforms to Gaussian for most distributions, roughly half the cases exhibit non-Gaussian tails in both winter and summer seasons. Most of these are asymmetric, with a long, roughly exponential, tail on only one side. The shape of the tail has substantial implications for potential changes in extreme event occurrences under global warming. Here the change in the probability of exceeding a given threshold temperature is quantified in the simplest case of a shift in the present-day observed distribution. Surface temperature distributions with long tails have a much smaller change in threshold exceedances (smaller increases for high-side and smaller decreases for low-side exceedances relative to exceedances in current climate) under a given warming than do near-Gaussian distributions. This implies that models used to estimate changes in extreme event occurrences due to global warming should be verified regionally for accuracy of simulations of probability distribution tails.