Coolant fans not working and causing the engine to overheat

Hello. I suspect that one or both of those fan motors are pulling too much power for the circuit. When you wire direct to the battery, you're reducing the electrical resistance so it doesn't burn up those wires. Hook it up directly again and let it run a few minutes. If the wires are hot to the touch, then the fan motors need replacing. Might as well replace any burnt looking wires as well.

Also, pull out the under hood fuse box and look for signs of charring.

Let us know what you find.