Q: How long do you let your car "cool down" before covering it?

Do you mean after being in the sun for a long time, or the engine being hot?...
 

I wouldnt say wait for too long or youd be out there for a long time, metal takes a while to cool down anyways, the cover wont burn or anything if the metal is slightly warm...
just my 2cents

No cool down needed
 

for the 4.2 or the 2.7t. Turbocharged cars normally require a cool down period so the turbo bearings aren't cooked in any remaining oil within the turbo. The 2.7t recirculates this oil. 97-01 A4 turbos do not have this feature so to extend turbo life, a cool down period is recommended. I've noticed my turbo glowing red after spirited driving. Normally a 2 minute cool down will elimate the glow.

Sorry, I should've been more clear. I'm worried about the hot hood and exhaust touching the cover.