Here's my advice. You have a bad PCM.
Your car seems to be doing exactly the same as mine.
1. Dying when hot, with no apparent reason, nor any indication that it is about to die. (No stumbling, no coughing, running rough, funny idle, etc)
2. ONLY does it hot.
3. Engine gauges peg at zero.
4. No trouble codes.
5. Crank sensor replaced.
Try this out.
Let it idle in the driveway till it fails. Turn the key off, and then try to restart. No gauges, no restart? Good, that's what we want. CHECK
Begin by disconnecting the battery for 30 seconds. Hook it back up, see if it immediately restarts. If it does, let it run till it dies, making note of how long it takes it to quit. Do this every time you restart it. NO RESTART SO ON TO THE NEXT
Next time it dies, verify a no-start condition, and run through these sensors:
Throttle Position DIDN'T START
IAC Motor DIDN'T START (PUT A NEW ON ONE ALSO)
Camshaft sensor (careful, this one is hard to get while it is hot) NO WAY TO GET TO IT
MAP sensor HOLD ON TO YOUR PANTS, FINALLY FOUND THIS DAMN THING, UNPLUGGED IT AND STARTED RIGHT UP, IDLED KINDA FUNNY, UP AND DOWN BUT RAN
With the key off, pull the connector for the sensor you are working with, and turn on the key. See if the gauges come back. Replace the connector if it does not, and move onto the next sensor. Theoretically, the sensor that you isolate, and gives you your gauges back will be the culprit. ONLY the crank, cam, throttle, MAP and IAC can short in a fashion to ground your PCM out to make it stop responding.
Once you get one that gives you your gauges back, turn the key off, plug that sensor back in, and start it and run it till it fails again. Remove that connector first to re-test.
What I think you will find is the same thing I have. The PCM is internally fried from living too close to the exhaust manifold for too long. But that should help you narrow it down good before coughing up the change for a new box.