So that's a 60A fuse, right? Either you are near the maximum current for an extended amount of time or there could be a problem with the contact area the fuse has with the fuse holder.
A very small contact area due to oxidation of either the fuse terminals or the fuse holder can cause overheating.
Deenergize the whole circuit ! and then have a look if oxidation might be the problem, if that's the case clean both parts with for example a metal brush.
as mentioned, check for contact corrosion on the fuse holder. If it's part of a disconnect, check your switch blades for corrosion and that your wire terminals are snug and free of temperature degradation. An ohm meter reading from input to output wire will give you some insight. Make sure all power has been removed.
If all looks good, replace your fuse. It may have been opened but fused by higher than rated short circuit current. In doing so, you must investigate if the fuse has adequate rating for the source, specifically in regards to short circuit current ratings.