Why do choc chip cookies change with different temperature butter?
It all comes down to "creaming".

When you mix granulated sugar with solid (cold or cool) butter (creaming), the volume increases thanks to little-itty-bitty bubbles in the fat. That creates a kind of leavening. The bubbles get bigger as the item bakes.

Melted butter doesn't do that at all, and very softened butter does it very little.

So, different temperatures of butter in the batter make for different cookies, even if everything else is the same.

For an added factor in your daughter's experiment, try butter flavored shortening. It has a higher melting temperature and added emulsifiers. Shortening makes for more, but smaller, bubbles.

Here's a pretty good blog on the subject of The Creaming Method. The article covers temperature at length.

See also: What is the purpose of creaming butter with sugar in cookie recipes?