Warm & Dry is always best. To that effect I usually either run the heat up in a room to approx 80 degrees, then turn it off when spraying and for the first 10 minutes afterward, Or...I use a itty bitty 50-60-85,000 BTU Propane Bullet heater and bake out the room surface, get everything really toasty warm (85-90 degrees) spray, the after the Screen surface has dried to a point where it has lost all sheen, I turn the heater on again for 10 minutes. After all that, I can usually put another coat on in just under 30 minutes.
On a whopper screen like yours, multiple fans used in a static, warm, Dry, dust free (as possible) environment would be best. Painting such a bugger would entail first priming the surface, sanding, re-priming again, lightly sanding again, then starting your spraying. Don't forget the Bucket Truck.
A valuable tool to have handy is a case of "Liquid Wrench". My current preference is Guinness Black Lager.