This paper investigates the relationship between rising global extreme heat exposure and deforestation. Combining global data on deforestation and daily temperature realizations at the one-degree grid-cell level from 2001-2019, we show that each additional degree day above 32 °C increases deforestation at the forest edge by 0.25 percentage points. These effects accumulate over time and are driven by tropical regions. Consistent with heat-induced declines in agricultural productivity as the driving mechanism, we show direct evidence that extreme heat reduces a satellite-based crop productivity measure and find that the effect is larger for the most heat-sensitive crops and the crop-country pairs with the most inelastic demand. We also show that this deforestation is accompanied by cropland expansion using both global satellite data on land use patterns and three rounds of agricultural census data from Brazil. Back-of-the-envelope calculations attribute about 2-3% of global frontier deforestation, and up to 15% in the Amazon and Congo hotspots, to recent temperature extremes. Taken together, our findings support the view that climate-induced productivity losses lead to intensification within regions rather than reallocation across regions.