The geometry of the bill (broad rather than slender) is exactly what one would expect to maximize the interior surface area and increase the evaporation potential.

The Toucan's beak appears quite heavy, but is actually light.  It is hollow, made of the protein keratin with thin rods of bone to support it – similar in consistency to a hard sponge.

A Toucan's bill is about 30 or 40 per cent of its total body surface area, so it's like you throwing out a sail and dumping all your body heat into it.  During an actual experiment, captive Toucans were used with an infrared camera trained on their beaks.  What was found is that as the birds got hotter, their bills glowed brighter on the camera images.  As they cooled, they began shutting down blood flow to blood vessels that run thick near the beak's surface.  The Toucan's ability to control heat-bearing blood flow to the beak, like adjusting a thermostat in your house, was one of the study's key findings.  So sensitive is the bird's internal thermostat that the beak lit up the research cameras to different degrees as the Toucans progressed through their stages of sleep at night.