I disagree with the "short" analysis, or the fuse would blow.
My reference is to where the wire is crimped on the back of the fuse holder. If several strands of wire are not properly crimped or have broken then the current being drawn through the remaining strands will cause them to get hot. Heat transfers through the blade portion of the holder and into the fuse. The fuse, being soft plastic, melts but the fuse does not blow.
You need to remove the fuse holder and inspect the back side of it where the wires are connected. My bet is you will immediately see the suspect wire with melted insulation and careful inspection will reveal what I'm talking about.