sounds like a coil
Sounds like your coil is dying. It gets hot, creates an open and dies because you lose spark. Then, it cools a while, makes contact again, and your off and running. Simple fix, about 40 bucks for an MSD blaster or similar.
To troubleshoot, get it to where it dies, then quickly pull and test the coil with an ohmmeter, it should be open. If you can heat the coil significantly while it's out of the vehicle, you could test this way also.
You can pull the coil and put it in a 200 degree F oven (lowest temp setting) for half an hour or so to simulate underhood temp conditons. If your real slick, you could have the ohmetter hooked up to it in the oven and watch it as the temp rises. But this might melt test leads and what not, use discretion if attempting this method. I would make some dummy leads out of high temp wire and run them out of the oven so you don't risk any of your ohmmeter test leads.
Depending on your budget and time, this method could take longer than just swapping in a known "good" coil and testing it in the same circumstances it is currently failing in. However, if you buy a new part and it's "not" the problem, most electrical parts cannot be returned, which is why troubleshooting may be worthwhile effort.
If not this, still sounds like a temperature related issue in a component going to or controlling the coil, like the ignition box.
I don't beleive it to be a cap and rotor issue or it would die and stay dead.