Question about variable-speed pumps

Hello everybody, I'm new here.. glad I found a place to ask pool questions.

So I am a new home-owner and my new house has a 29K gallon in-ground pool. I have never owned a pool before, so the past few weeks have been a learning experience for me. The pump is a Hayward 1HP single-speed pump. I've been thinking about upgrading to a variable-speed pump for 2 reasons:

1. Electric bill
2. Safety features??? (this is actually my question):

My safety problem: One time when I was at work, my pump lost it's prime, but kept turning. By the time I got home, the pump was too hot to touch, and the water in the basket was near boiling temperatures. I let it cool, unplugged it, and checked the impeller by hand -- it was not stuck, so I re-primed the basket with water and it started pumping again -- as happy as could be.

So my question is: Are these new variable-speed pumps smart enough to realize they are overheating or that they lost suction? If so, will they shut off? Or will they do what my dumb pump did and just keep on turning until they burn out or start a fire?

Thanks