Hi Mike,
the heating of the basket would occur when water is in it and not moving, not when dry. What happens is when the output is blocked and water isn't moving, a lot of the energy the motor puts out is transferred to the water by the impeller. Basically the old lab experiment where you stir a container of water vigorously and measure the temperature rise to determine how much energy you put into the water. With the power a pump motor can put out you can actually boil the water and regular PVC starts softening a little before boiling temps. Thus the integrity of any threaded PVC joints into the pump housing can be compromised. You can use vaseline to check for leaks at the joints. A lot cheaper than silicone grease and as long as you wipe it off and remove the last traces with an alcohol soaked paper towel you'll be ok. I don't think vaseline should bother the materials anyhow but leaving a residue will collect dirt. Don't use it on O-rings and seals though, like the basket lid seal. Use silicone grease.
Since you have ruled out blockages I believe, the way it happened it sure sounds like an air leak. Just a matter of finding it. One more thing to try to get some idea if the pump seal is OK is to take off the basket lid and using a 5 gallon bucket pour water into the basket and let the pump circulate it. Maybe a couple garden hoses instead to provide enough water to build up some pressure. If you see any dribbles coming from areas that are normally dry then that could give a clue.
Al