The global average temperature of the Earth has increased, but year-to-year variability in local climates impedes the identification of clear changes in observations and human experience. For a signal to become obvious in data records or in a human lifetime it needs to be greater than the noise of variability and thereby lead to a significant shift in the distribution of temperature. We show that locations with the largest amount of warming may not display a clear shift in temperature distributions if the local variability is also large. Based on observational data only we demonstrate that large parts of the Earth have experienced a significant local shift towards warmer temperatures in the summer season, particularly at lower latitudes. We also show that these regions are similar to those that are found to be significant in standard detection methods, thus providing an approach to link locally significant changes more closely to impacts.