The intensity of moist convection is an important diagnostic of climate change not currently predicted by most climate models. We show that a simple estimate of the vertical velocity of convective updrafts in a global climate model reproduces observed land-ocean differences in convective intensity. Changes in convective intensity in a doubled CO₂ simulation are small because the tropical lapse rate tends to follow a moist adiabatic profile. However, updrafts strengthen by ∼1 m s⁻¹ with warming in the lightning-producing regions of continental convective storms, primarily due to an upward shift in the freezing level. For the western United States, drying in the warmer climate reduces the frequency of lightning-producing storms that initiate forest fires, but the strongest storms occur 26% more often. For the central-eastern United States, stronger updrafts combined with weaker wind shear suggest little change in severe storm occurrence with warming, but the most severe storms occur more often.