why would a new set of headers become so hot that the steering shaft cover melts?

The headers may need to be wrapped with heat wrap.

Headers will naturally run hotter than your stock exhaust manifolds due to the thinner gauged tubing used. They can't absorb the heat as well as the heavy castings. Also it's not uncommon to run into problems like you mentioned with melting parts under the hood. Like any aftermarket part, other mods may be necessary to make them work/fit. I would follow Mikes recommendation and locate some wrap. I've had to take the plastic covers off in the past because of this problem.