The microphysics of molecular hydrogen formation has an influence on galactic-scale star-formation rates over cosmic time. H 2 is the cooling agent needed to initiate the cloud collapse regulating the star-formation efficiency. H 2 formation is inefficient in the gas phase under typical interstellar conditions, requiring dust grain surfaces to act as catalysts. Small carbonaceous grains with sizes from roughly 4 to 100–200 Å, including polycyclic aromatic hydrocarbons (PAHs), have been shown to increase the H 2 formation rates due to their large surface-to-volume ratios. H 2 formation rates on PAHs were previously thought to reduce above temperatures of 50 K and H atom recombination was believed to be highly efficient only below 20 K. Until now, both laboratory experiments and theoretical modelling have suggested that H 2 cannot form on grains with temperatures above 100 K. Here we report evidence, through direct laboratory measurements, of the highly efficient formation of H 2 at temperatures up to 250 K on carbonaceous surfaces mimicking interstellar dust. By pushing their formation towards warmer temperatures, the H 2 molecules could start contributing substantially to the cooling of warmer gas (temperatures of roughly 50–250 K). This will have a marked impact on our understanding of H 2 formation in nearby galaxies and its efficiency in high-redshift galaxies where the Cosmic Microwave Background already pushes dust temperatures to more than 20 K.