Relay overheating 308GT4

Clean/replace all of the male/female plug contacts in the circuit from the back of the bulb to the relay panel. High resistance at each of the numerous plugs in the circuit will require the relay to pass more current and get hot.

Once they get very hot, the contact points in the relay itself will also show high resistance across them and requires replacement. Male contacts at the plugs are easily cleaned, female requires replacement as there is no way to properly clean and re-tension those.

Set out your wiring diagram on the table, identify every connector in the circuit and address them all. The end result is no better than the weakest connection.

 

Another thing to check is what wattage headlight bulbs have been installed -- higher power bulbs (e.g., 80W or 100W vs the stock 55W) will greatly increase the heating because the heat generated at a bad connection, or the relay contact points, increases by the ^2 of the current (i.e., an 80W bulb more than doubles the heating, and a 100W bulb more than triples the the heating).

Also, this type of problem has a sort of positive feedback characteristic -- i.e., you have a bad connection (with a little resistance), so it runs hotter, which causes the parts to oxidize more and/or lose their "springiness" (loosening the connection), which raise the resistance a little more, which makes it run even hotter, etc.. In addition to making sure that the connections meant for assembly/disassembly at the relay are in good condition as Dave suggested, you might also consider soldering the female metal terminals in the relay socket that connect to the 30 and 87 terminals on the relay to their respective wires so they are not relying on just the mechanical swaging for a good (low resistance) connection to their corresponding wire (i.e., this supposedly "permanent" connection may have been damaged).

 

The only heat coming from a relay is generated in it's coil and that's no more than 2 watts causing the relay to be warm but not hot.

Those above have referred to contact resistance heat, coming from either contacts the relay plugs into, or relay contacts.

Were I you, I'd remove the plastic relay cover and findout which. Two relays are in charge of bucket lift motors only and other gets main headlight current.

Another test would be to unplug one headlight and see if the heat subsides. In which case you may be using a relay with insufficient current carrying capacity. Remember, these relays come in two flavors...30 amp and 40 amp. Not mentioning cheaper substandard Chinese who knows what.