An engine needs this to run:
air, fuel, spark, proper timing of the fuel and spark.
Over the web its difficult to tell you which one is missing.
You will need to figure that out.

I'm guessing a sensor or control module is getting cooked and failing
until it cools.  Have you checked on the ignition control module? It's
hard to nail down the problem when it only does it when it's hot.  I
wouldn't rule out a bad alternator, either..

Did you change the filter?!?!

Your car starter has become your car stopper?   I don't think so.

It's probably fine.

What was wrong with the fuel pump, and what defects did it show when
tested for pressure and volume?  Of course it was tested for those
things because it makes no sense to replace expensive parts otherwise.

Were the fule injectors dirty?  Considering the car is a 1997, I doubt
it.

You paid to have your car fixed, and unless they told you they didn't
fix it and charged you only a diagnostic fee, they owe you either a
repair or refund.

You want to know if your engine stops because of lack of fuel or lack
of spark.  To see if this is a fuel problem, squirt propane or
carburetor/throttle body cleaner spray into the intake (preferrably
with the air filter still in place so it can block any flame from
blowback) while a friend cranks the engine.  If the engine runs when
you do this but doesn't run otherwise, then you have a fuel delivery
problem, and your ignition system is probably OK (it could be marginal,
but I doubt it, unless the engine has been idling roughly or has been
weak).  To check spark, remove a spark plug wire and connect it to
another spark plug (even a cheap one will do, so long as it fits the
connector) and hold its metal body against some bare metal (engine,
frame).  While a friend cranks the engine, listen and look for spark
(may be hard to see in strong sunlight).

I'm going to suspect a bad electrical connection, possibly a ground,
related to either the fuel pump or ignition system (including the key
switch), or a bad ignition module, but realize I'm only guessing, so
don't replace anything that doesn't fail testing, unless you can find a
TSB (technical service bulletin) saying it's a problem device.

If you diagnose this yourself, get a GM or Mitchell manual since other
books don't cover fuel and ignition systems very well or may even
provide wrong information (troubleshooting information may even apply
to carburetors instead of fuel injection).  Also look at web sites that
specialize in GM cars, such as www.chevyforums.com

My guess would be the fuel is vapourizing in the lines before
reaching the injectors, thus no fuel. When you let it sit the lines
cool down and the fuel gets through until the lines get hot again.
My two cents . . . anyway. . .