"I wonder if converting large amounts of the heat energy into electric energy would cool off an area?"

Nope.

"I am reminded of “Energy is never created or destroyed. It just changes form.”
But there are always losses in the transformation in the form of heat energy.

"Living in a place that gets very hot, I would love to see heat energy converted into electric energy. "

In order for this thing to work it will require a source of cool air which then gets tranformed into hot air. This thing would add heat to the environment- it takes energy that normally would mostly reflect back into space. This thing is powered by cold as much as it's powered by heat- needs a difference in temperature. It would work best where you had lots of solar power and lots cold stuff you wanted to heat up- like at lunar poles or the ocean (if you wanted warmer sea water- say in order to convert into fresh water).