+1 on the current issue. Wires get hot mostly due to excessive resistance in the circuit. Blame for that can be old and decayed wire, bad connections, bad grounds, wire that is undersized for gauge and application, and old components like the motor mentioned above.
As for the addition of an aftermarket relay
View attachment 154575
This picture is of a typical 5 pin relay socket. Basically all a relay is, is a type of switch that uses a low power circuit to initiate or close a second circuit in the relay that is designed and built to handle power delivery to a high demand circuit, such as power window motors, or windshield wipers or a starter. For the sake of conversation here, make the assumption that this relay is being put in a typical GM starter motor circuit. In the above picture there are two pins designated #85 and #86. These constitute the low power side of the relay. In a factory design, power to the starter solenoid and starter motor goes through the key switch before it gets to those destinations. The further current has to travel before it reaches whatever it is expected to operate, the higher the resistance will be in the circuit and the greater the voltage needed to deliver enough power that whatever is being actuated will actually work. With the relay wired into the starter circuit, the key and its wiring no longer have to deal with heavy voltage or current. The power would come from the battery, but instead of going to the key directly it would go instead to pin 86 and then, when the key was turned to start, the relay would close and power would flow to ground, aka 85. The heavy duty or high power side of the relay is handled by # 87/87A, and #30. As shown in the diagram, #30 is the power in side of the relay. In the starter motor example, this would be power coming directly from the positive side of the battery. When the key is turned and the relay is actuated, the second high load circuit is activated that sends the power coming in on 30 out again on either 87 or 87A (if multiple events need to occur at the same time) In my example, that would be power going to the solenoid and the starter motor to get the starter cranking the engine over.
Here's the thing. The key side of the relay doesn't need heavy gauge wire, it can now live quite happily with the stock gauge wires it was fitted with by the factory as they no longer have to deal with high/heavy current or voltage. The power side of the relay can be wired using heavier than stock wire, such as 12 or 10 ga. wire, as opposed to the stock/OEM 26 or possibly 14 ga that the harness was laced with. Moreover, the wiring for heavy side of the relay also becomes shorter and more direct because it no longer has to travel into the cabin and to the switch and wherever else before it finally gets to the starter. This translates to less resistance in the heavy circuit due to it being both shorter and made of a higher gauge wire. Current flows more easily and less voltage is needed to make the delivery. The net consequence is that the starter gets more power to spin up more quickly and strongly, creating less internal heat due to being able to work more efficiently and the engine turns over and fires sooner. The battery is also happier because the draw on it is less over time meaning it takes a shorter amount of time to recharge after the engine is running.
Basically you can insert a relay into almost any circuit where there is excessive draw and current drop. If you feel like being contrary, 85 and 86 can each do the others job; they are not dedicated in terms of which handles power in and which is ground. And for those who grumble that all this is well and good but how do I figure out the numbers if I don't have the cute socket or similar shown above? if you flip the relay over to display the pins, you will discover that each pin has a number sitting beside it. As for 5 pin versus 4, the 4 pin just has one #87 pin, meaning it is designed to handle only one activity or event. The five pin would see action in a high/low headlight situation with one 5-pin handling the low beams and a second the highs.
Enough. This takes longer to illustrate than it does to fabricate and install the harnesses and hang the relay somewhere. Bleah.
Nick