I would suspect a potential ignition module failing at higher temps. To check this, I'd invest in a 'gap type' spark tester. They're inexpensive and available at most auto parts stores. When the unit dies, put the tester in line with the spark plug wire and and see if you still have spark. If not, then you need to verify it's not the kill switch circuit from preventing spark vs the ignition module itself being bad. Basically, you'll want to disconnect the kill switch wiring so that you know it isn't causing the lack of spark. Given the symptoms you describe, I doubt it's kill switch wiring related. It's important to rule this out though so you don't buy a new ignition module and find out that's not the real problem
So give that a go and let us know how you make out and we can proceed from there. Good luck!