Check the owners manual. Usually they say it is OK in warmer weather.
I don't doubt that some owner's manuals state that, but its kind odd reasoning. The weather has much more effect on lubrication during cold engine startup--when the 5w viscosity comes into play.
Engines operating temps are largely controlled by the thermostat, not the weather--when the 20w or 30w is in effect.
It would make more sense to state that a 10w/20 (if one existed)can be run in warm climate than a 5w/20