A lava flow extruded on the surface of Venus cools by radiating heat and by advecting heat upward by thermal convection. Unlike on other planetary bodies, these processes are intimately coupled on Venus because the dense CO2-rich atmosphere has strong absorption bands in the infrared. Relative to a transparent atmosphere, absorption (and emission) of radiation within short distances above a lava reduces the radiant heat loss and substantially diminishes the vigor of convection by dampening the thermal gradients within the boundary layer. For these reasons, lavas on Venus cool significantly more slowly (30--40%) than they would if the atmosphere were transparent in the infrared, as assumed in previous calculations. Considering these effects indicates that lavas on Venus cool more slowly than their equivalents on Earth rather than more rapidly as previously estimated. The reduction in cooling rate due to the suppression of convection by radiation extends our understanding of how some lavas on Venus reach extraordinary lengths, on the order of a thousand kilometers, before solidifying.