Exploding Duct Theory - Redux

Shouldn't belly button lint be going down the bathroom shower drain?

The PVC isn't really an improvement over galvanized, with no appreciable advantages and some major disadvantages with potentially serious problems. Dryer's create massive amounts of highly flammable lint dust, usually due to overdrying, and the static electricity charge can be sizable. That's a really bad combination.

If you're set on using PVC, design it like a wood dust collection system with grounding wire, make sure you clean the pipe regularly (should be done regardless of vent material), don't overdry the clothes and use fabric softener sheets in the dryer which greatly reduce static build-up.

Will the PVC melt?

yeah. *DON'T* put belly buttons in the dryer. Hang them outside on the line.

Problem solved.

your personal situation, you may want to check with your local authority and see if it would present any code problems in your area.