[patrickt]

As a general rule, a loose or crappy connection reduces current, because it's an increase of resistance. But that rule doesn't apply to electric motors because they're not completely a resistive load. I can see how a voltage drop across a bad connection would cause the motor to lag and, in turn, pull even more current. That, in turn, heats up the bad connection and adds more resistance, which results in higher amperage. That cycle continues until you blow the fuse. If clamping an ammeter around the feed to the fan, when it's really hot under the hood, shows an unusually high current (like high 20's) then a voltage drop test will spot the resistance point in a jiffy.