Quoted from Chalkey:
Would putting them in front of a fan help at all?
Polyurethane does not dry as in air dry. It dries by catalytic conversion. As soon as you add your catalyst and mix it up the conversion has started. There is a term called pot life which is low long the paint will remain in pourable form in your paint reservoir. Leave the paint mix in your paint gun beyond pot life and if you are lucky will only have to spend a couple of hours digging it out of all the nooks and crannies in your paint gun. You will only fail to ignore pot life warnings one time.
Depending on temperature, the pot life could be as short as 30 minutes on a hot day and as long as 2 hours on a cold day. But once you apply the paint it will be dry to the touch in 20 minutes; That's dry, but not cured.
The conversion rate depends on the amount of heat. I.E. it will cure faster on a hot day as opposed to a cold day. And lighter coats are going to cure somewhat faster as opposed to thicker coats where it is going to take awhile for the 'buried" paint to "dry" completely (see pot life).