93 Corolla - Vapor lock?

It is not vapor lock.

If the engine is stalling when idling or coming to a stop from a higher speed, the most likely culprit is a gummed up idle air valve.

Another possibility is that the MAF or MAP sensor is dirty.

Also check to make sure the EGR valve closes.

When was the last time the spark plugs, ignition wires, cap, and rotor were changed, and what type of parts were installed?

Another possibility is that all that fuel injector cleaner damaged the fuel system by dissolving a flexible line, which clogged the fuel filter or injectors.

It wasn't while coming to a stop, just in real hot weather, in the mid- upper 90's, when driving after the engine was hot.

In the evening last night, when it cooled down outside some, it was fine for 5 hours straight.

I put in iridium plugs about 6 months ago, don't recall the last time on the rest.

Wouldn't it be doing it all the time then?

I'd still start with the idle air control valve.

It is possible that the ignition wires are marginal, and the extra heat raises resistance enough to cause trouble, but it would more likely manifest itself as a miss at higher RPM than at lower RPM.

Likely yes, and at higher engine speeds more than at lower engine speeds, which is why I listed that possibility last.

What's it called here?:

It could be a bad coil

Autozone also calls it an Idle Air Control (IAC) valve.

Look under the "Drivability and Engine Controls" link, then under the "Electronic Engine Controls" link. Check the IAC valve as described.

I found out more about this since before.

It only happens when it's hot outside ( above 90? ) and the engine has been sitting hot for awhile too, then we start up the car again.

It sometimes stalls when I drive off that way, and when I pull over and try to restart, it won't, BUT if I turn the ignition ALL the way off and restart, it will, and runs fine for hours after that.

Is that weird or what?

This reminds me of a problem I had with one of those Chevy LUVs with the Izuzu engine. The engine would just die after some time of driving at operating temp. It turned out to be the electric fuel pump. There is a built in fail safe that kills the fuel pump if the temp. sensor senses the engine is too hot. Over time the sensor failed the fuel pump at lower tempertures. I met someone about 10 year later that described the same problem to me. But what you describe is happening on hot days while the car has been sitting. One trick I have always done in the summer to prevent vapor lock is add a quart of kerosene to at least

10 gallons of gasoline. With more ethanol in the fuel vapor lock is a more common problem.

After reading the symptoms, I think you should start by checking the IAC valve and the EGR valve

We were driving down the highway at 8:30 ( around sundown ) and it stalled briefly and then kept going with no problems again, the rest of the trip. It was like a stuttering bump we felt, then it just resumed.

I gotta get it checked out.