The power demand for the cooling fan is too large to operate off the circuit box, Always use a relay with cooling fans.
The relay switches the power on and off to the fan, the 12VDC+ is sourced at the battery through a fuse (battery + is usually picked at the starter), the relay is controlled by the ignition switch and fan switch (fan switch is ground). The relay's coil draws very little current, sourcing its coil 12VDC+ through the ignition, with the fan temperature switch supplying the relay coils ground.