A direct short should blow the fuse immediately. Since this fuse holds up for the short term I suspect the fuse blowing is caused by something with an abnormally high current draw. The most obvious thing would be the cabin blower motor. Current draw on those can skyrocket with age and miles.
The shop should have checked the blower current draw with an ammeter. The blower can be faulty and still move plenty of air with no noise whatsoever.