Okay, a heat issue it seems. Have to tried to see if you are loosing spark or fuel when it stops? That would certainly guide the possibilities a lot. When it stops, crank it over and see if you have spark to all cylinders. If not, you have an electrical problem, if you do have spark, check for fuel. You can buy a little spark tester and test each cylinder for spark when i quits. Most folks buy one like this and it works great for such things. They cost $10 dollars or even less at most auto parts stores.
Get one and see what is happening. Then post those result back here.
