If it's stalling because the battery is discharging from the alternator not charging or under charging that's one thing. If the system is charging fine and the car stalls. You have an entirely different problem.

As for not starting until it cools off...show me a Firebird owner and I'll show you a "No start when Hot" issue at some point in their lives.

Big battery cables, 1 Gauge in my case, solved that issue using an Autozone remanf. starter.