What would cause the fusible link on a 2001 Toyota Solara to burn out?
Any time a fuse link burns out one should suspect a LARGE short condition in the harness. Shut off all accessories and pull all fuses from the fuse panel. Take NOTES or replacement will be a pain. Disconnect battery if connected, Use a DVM and check the resistance of each accessory at the fuse side to ground. A low or zero ohm condition indicates trouble in that circuit. Also check from the alternator B+ to the alternator body. A low reading here would make one suspect the alternator has an internal short. Also check for a failed/shorted starter cable or starter.