The exhaust gets much hotter than you would imagine when the car is being driven under a load. Not to mention carbon soot being blown about.

The short story is not to drive it until fixed.

If you really must drive, a sheetmetal shield formed over the top of the muffler would be a acceptable temp fix. ( sort of like a super sized exhaust tip that is open on the bottom, )

Last year the tail pipe on my gas pickup rotated to a position above the bed side body line. ( a hanger broke allowing the exhaust to flex then rotate ). The paint burned off and completely melted the tail light and wiring.