Thanks for posting about this, @ElsieD. My mom had one when I was growing up and it was great for shallow frying and did a good job of maintaining temp. It was also great for pancakes. I've never had one myself but was thinking it might be handy.
The ones she had did have the "heat ring" that @lindag mentions but must have distributed the heat fairly well as there wasn't a problem with even cooking.
Edited to add that this is the one I was considering. The base can fit inside the pan to save storage space (though that can apparently scratch the non-stick coating) and has pretty good reviews. It's rectangular, so it doesn't fit your need for a square pan.
