A solidly crimped and assembled to specification J connector should not emit any heat.
Actually, with power connectors, it's all about the heat. Some of Molex's high-power connectors don't even have a "current rating" per se, just a family of curves showing temperature rise versus current flow. It's up to the engineer using the product to keep temperatures at safe levels in his equipment. When a manufacturer does give a current rating, it's based on the temperature rise curves, together with what the manufacturer thinks will be the worst-case circumstances his connector will experience. In reality, if the temperature isn't excessive, neither is the current.
Wires are no different. We talk about the "ampacity" of wires, but that's really about heat too. 8AWG wiring is 'rated' for 40 amps, but that's based on only a 30C temperature rise above ambient. Regular THHN-insulated wire can handle 90C, so 45C rise is generally quite acceptable, at which point 8AWG wire can handle 50 amps. A good chart is located at
http://www.cerrowire.com/enginering . Note that we're talking about free air here -- putting wires in an insulated area or packing several of them in a chase or conduit can require considerable derating from these values.