applying varnish to wood in the sun
Urethane doesn't "cure". It dries as the solvent (which may or may not be water) evaporates. It isn't like masonry where time and moisture are critical. 

There's no problem applying urethane in the sun other than the challenges it poses to the actual application. Very quick dry times mean less time to get good coverage and work out runs. 

Never apply heavier than a minimal thorough coat. Apply liberally, then spread well, leaving just barely a glossy appearance. Multiple thin coats are much better than heavy coats, which will sag and run.