Car won't start after running out of gas

Remove fuel cap and put your ear to the fill hole, have someone turn the key to the Accessory position. Can you hear the fuel pump humming? If not, check your fuel pump relay. If relay is good, odds are the running it out of gas may have been enough to push it over the edge. It's a 20 year old pump after all. If your model has a Auto Shut Down (ASD) relay, check that also.

The gas cools the pump, and it doesn't 'know' there is nothing to pump and burns up

Well completwly running tank dry is not good. It will suck dirt from tank then will eventually clog causing u to buy a pump. After running out of gas dont try and crank over put gas in and pump key three four timea to get primed then should fire right up