I saw a Modern Marvels episode last night on "Sticky Stuff". They featured a powerful acrylic foam tape from 3M: the VHB Tape.
Apparently this stuff is weather resistant and is more structurally sound than rivets for impact and heat expansion.
Here's a link to the 3M product website.
The cost may be the limiter: the cheapest is about $1.25/yd. for the 1/4-inch wide, 15-MIL application. It goes up from there in tensile strength width, color, and thickness. With a range of -40 to 200F, this might be a good applicator for grille blocking environs.