Does the 14 gauge wire run from the battery to the relay, the relay to the lights, or to the relay to actuate it?
No matter which it is, the resistance of the wire is causing the current passing through it to generate heat, which is normally an indication that the wire diameter(gauge) is too small. Just to be on the safe side, I would utilize a larger diameter wire(smaller gauge number), which will allow the current to pass with less resistance, and therefore, less heat generated.
Another source of heat can be the connection at the end of the wire. Most installations use crimp-on connectors, which are OK for applications that don't experience movement, vibration, or aren't exposed to corrosive conditions. The way to obviate the above potential problems is to solder all connectors, thereby eliminating the possibility of increased resistance at the connector. It also provides a much stronger joint, and passes current much more readily.
Keep in mind, the longer the wire or the smaller the wire, the greater the voltage drop due to resistance. The greater the voltage drop from one end to the other, the less current you can pass through the wire, and the less bright your lights will be.
Just use some larger diameter wire and solder your connections and you should be allright.