Extreme temperatures have warmed substantially over recent decades and are projected to continue warming in response to future climate change. Warming of extreme temperatures is amplified over land, with severe implications for human health, wildfire risk and food production. Using simulations from 18 climate models, I show that hot days over tropical land warm substantially more than the average day. For example, warming of the hottest 5% of land days is a factor of 1.21 ± 0.07 larger than the time-mean warming averaged across models. The climate change response of extreme temperatures over tropical land is interpreted using a theory based on atmospheric dynamics. According to the theory, warming is amplified for hot land days because those days are dry, which is termed the ‘drier get hotter’ mechanism. Changes in near-surface relative humidity further increase tropical land warming, with decreases in land relative humidity being particularly important. The theory advances physical understanding of the tropical climate and highlights land surface dryness as a key factor determining how extreme temperatures respond to climate change. Climate change warms extreme hot days over tropical land more strongly than the mean temperature as hot days are dry, according to a new theory and analysis of global climate models.