does an external power pack reduce overheating
Yes, the power supply, tube and electronics all generate heat. When any flash is being recharged, a very large current is drawn from the batteries or power source. This is why batteries get warm. This larger current draw also heats up the electronics.
You can pop off a few high power flashes and not notice the heat but if you keep going you will feel the heat.
If you need a lot of high speed flashes, it's best to bump up the ISO and use faster glass. This way you will be using less power per pop. And because you are not draining the capacitors all the way you will also get faster recycle time.