Just in case anyone takes this the wrong way, part of the purpose of over current protection is to keep wires from melting, so if your protection and the thing you're trying to protect both melt at the same time, your protection isn't really working.
Isn't that rating when the wire insulation catches fire and not when it melts? Copper can stand a much higher temperature that anything surrounding it, so the wire might survive long enough to cause the thicker wires to catch fire.
This made me realize I have no idea what fuses are.
In electronics and electrical engineering, a fuse is an electrical safety device that operates to provide overcurrent protection of an electrical circuit. Its essential component is a metal wire or strip that melts when too much current flows through it, thereby stopping or interrupting the current. It is a sacrificial device; once a fuse has operated it is an open circuit, and must be replaced or rewired, depending on its type.