OP, is this your first time using a DA?
If so, the overheating may be related to some user error. Heat is a byproduct of the friction during the polishing process. While the motor of the polisher creates some heat, most "overheating" problems start at the pad, and travel through the backing plate - through the spindle mechanism into the machine.
Some things that make a polisher run too hot:
1. Using too much buffing liquid
2. Using too much downward pressure.
3. Running at top speed with significant downward pressure for significant intervals.
I wouldn't be so quick to blame it on the cord. All you have to do to rule out if an extension cord is a problem is feel the temperature of the cord. If the cord is quite hot - that could be a sign the cord is an issue.
That being said, me and like a zillion others have used the GG6 with whatever orange extension cord I've had laying around and never have had an issue. Hopefully your not using an inside extension cord, but if your using an outdoor style one you are like good unless it's defective or damaged.
4. BP rubbing on the shroud.
5. Operating the machine at very high ambient temperatures.