I'm looking at the wiring diagram in my haynes manual, and it looks like:
brown - relay coil positive, hot in run
green/white - relay coil negative - ground to turn fan on in run
red or orange: fan relay power
black/red - fan power wire, only hot when relay is "on" (green/white grounded)
If you've got a multi-meter, unplug the fan relay, and make sure the relay is getting power. Check voltage across the brown wire and chassis for 12v when the ignition is on, and across the red or orange wire and chassis for 12v in any key position.
If the brown wire is getting hot, then something is drawing too much current through it. The relay coil shouldn't draw nearly enough power to make the wire hot. If the fan motor is worn out, it can draw too much current and make the larger gauge wires (red and black/red) hot, but it shouldn't affect the brown one.
The fan gets it's power from the main fusible link near the battery, I would also check and make sure that's not blown.
I found a wiring diagram which may help:
http://album.hybridz.org/data/500/92-7730v8tpi-4.jpg