Connections are the weak point.

Even if the wire gauge is correct, the plug and outlet interfaces can add resistance. That resistance turns into heat.

Extension cords are simple: the copper wire is one spec, but the prongs, the receptacle contacts, and the point where the wire meets the plug blade all introduce potential trouble. A cheap cord might have thin or poorly crimped connections inside the plug. A worn outlet can have springy contacts that don’t grip the prongs tightly. Corrosion or dirt on the prongs also builds resistance.

The heat isn’t coming from the wire itself—it’s coming from the junction. You’re basically running current through a tiny, loose handshake between metal parts. That generates heat, not the load capacity. Even a 14-gauge cord rated for 15 amps will heat up at the plug if that plug doesn’t have a solid connection.

Check the outlet first. If it’s loose, replace it. If the cord’s plug feels warm to the touch after moderate use (a space heater, a power tool), toss the cord. Not worth the fire risk.