I can certainly give that a go, however I don't believe that's the cause. The symptoms I'm having are that the bike starts up cold no problem. Then I ride and the battery drains where it then stops. If I try and start the bike up again, the starter motor struggles. If I short the connection between the solenoid, the same thing occurs and continues to do so until the bike is cold.
I'll give it a shot anyway because I'd rather eat my words and ride than not.
Are you saying that the bike starts ok after it has cooled down without re-charging the battery or using jumper cables ? - If so this is not a charging issue, a battery simply stores electrical energy so once you have used it you need to replace that used energy (re-charge it) unless there is some "alchemy" afoot a battery won't re-charge itself.
Once the bike is running the electrical system runs from the generator and the excess is used to top up the battery (if your battery was flat and you bump started the bike by rolling it down a hill it would continue to run), therefore unless the battery is totally "goosed" it won't cause the bike to stop once running and it certainly wouldn't be able to re-start under it's own steam. I am with Forrest on this one, I believe your issue is corroded electrical connections causing a resistance.
The reason I think this is simply, when you have a corroded connection it causes resistance - a by-product of resistance is heat build up - heat causes an increase in resistance - which in turn generates more heat - this cycle continues until the resistance is so great that not enough current can flow for the bike to work. When it dies and you turn it off there is no current flow so the resistance (corroded connections) cools down and again allows current to flow and the bike to re-start. At this point the whole process of heat build up starts all over again.
This is the most common cause of the type of fault you are describing (breaks down every 15 minutes - re-starts after a short while.
Just out of interest have you checked that it's not a mechanical issue causing the motor to tighten up when hot ??