1997 Chevy Lumina Car won't start when hot

When you say it acts like the battery is dead, do you mean the starter doesn't crank at all, or it cranks but it doesn't start?

If it cranks but it doesn't start, I would start by checking for sparks when your engine is hot and you can't start the car. If you don't have sparks, I would suspect a bad cps (the sensor goes open at high temp which 'kill' the car until it cools down). It could also be a bad ignition module and/or ignition pack.
If you do have sparks, let me know, and I'll think of something else.

Now, if the starter doesn't crank, check for voltage at the starter, and let me know what you get.