Heat extremes have been increasing both in frequency and in intensity in most land regions of the world, and this increase has been attributed to human activities. In the last decade, many outstanding and record shattering heat extremes have occurred worldwide, triggering fears of a nonlinear behaviour or an 'acceleration' in the development of heat conditions, considering the warming level when the event occurred. Here we show that the evolution of yearly temperature maxima, with return periods (RPs) above 10 years, consistently shifts with global temperatures and does not significantly depart from this behaviour in recent years or decades when considered globally or at the scale of continents. This result is obtained by using a classical statistical event attribution technique, where the assumption that the distribution of block-maxima extremes linearly shifts with global warming is tested across years and world land regions. However, the pace of frequency change is large, with the probability of heat extremes exponentially rising and nearly doubling every decade since 1979, particularly when considering events with a RP of about 10–50 years in 2000. This makes the climate of a decade ago unrepresentative of today's climate. Our results overall mean that we do not expect events like the recent outstanding extremes to undergo nonlinear changes, despite fast changes. They also show that assumptions underlying attribution techniques used in many recent studies are consistent with recent temperature trends.