With ongoing global warming, climatologies based on average past temperatures are increasingly recognized as imperfect guides for current conditions, yet there is no consensus on alternatives. Here, we compare several approaches to deriving updated expected values of monthly mean temperatures, including moving average, exponentially weighted moving average, and piecewise linear regression. We go beyond most previous work by presenting updated climate normals as probability distributions rather than only point estimates, enabling estimation of the changing likelihood of hot and cold extremes. We show that there is a trade-off between bias and variance in these approaches, but that bias can be mitigated by an additive correction based on a global average temperature series, which has much less interannual variability than a single-station series. Using thousands of monthly temperature time series from the Global Historical Climatology Network (GHCN), we find that the exponentially weighted moving average with a timescale of 15 years and global bias correction has good overall performance in hindcasting temperatures over the last 30 years (1984–2013) compared with the other methods tested. Our results suggest that over the last 30 years, the likelihood of extremely hot months (above the 99th percentile of the temperature probability distribution as of the early 1980s) has increased more than fourfold across the GHCN stations, whereas the likelihood of very cold months (under the 1st percentile) has decreased by over two-thirds.