Walls and Ceilings - drywall ceiling in basement- heater ducts

In my basement, I am trying to frame around my heater ducts on the ceiling of my basement. I have drywalled the whole ceiling up until the part where those big metal sqare heater ducts hang down about 15 inches or so...
I have to make a frame around these heater ducks to mount the drywall.

I have to drywall around the heater ducts, and i was wondering how dangerous it is if the drywall is touching the heater duct at all. I know the heat is only about 75 to 80 degrees, but is that normally taken into consideration?

We normally use a zip tool for cutouts around vents, lights, etc and you'll routinely end up with like a 1/8" gap around them that is covered bu the trim grate. In short I don't see a problem with your situation.

You can place drywall directly against the duct work with no clearance. The only thing that needss a clearance is the vent stack for the heater (if you have a gas or oil heater, or water heater). If you use 5/8 drywall it has a larger span and you can often avoid framing below the duct. Fram on each side and fasten the drywall from side to side. If you need framing because the sapn exceeds 24 inches, use 1x4 flat every 12 inches and 3/8 dywall to reduce the headroom loss.