Why does cheddar cheese melt but feta cheese retains its basic shape?

Just was wondering what makes feta cheese so different from your basic pizza cheeses? Cheddar you add heat and it reduces to a yummy goo, feta just keeps its basic shape and burns.

It boils down (pun intended) to fat content. Fatty cheeses like cheddar, mozarella and Swiss melt rather easily, while lower-fat cheeses like Feta and parmesan don’t. It’s actually the fat that melts, you see.

Actually, Feta cheese often has a higher fat content than Cheddar:

See this article for the real reasons why: http://www.cdr.wisc.edu/pdf/Winter00.pdf

actually fat content plays only a small part of the cheeses properties. Much more important is the protein structure see http://www.foodsci.uoguelph.ca/cheese/sectiona.htm .
E.g. both mozzarella and camembert, melt easily, and have fat contents of 23-24%, similar to halloumi which doesn’t. The protein structure is determined by the source (cow, sheep, goat), how it is coagulated (acid, rennet), the final pH, and how it is cured and for how long.

Actaully, feta will melt if you do it right; put a chunk in a bowl and microwave it for a minute and it becomes a liquid the consistency of vichyssoise (until you burn it). Farmer’s cheese generally won’t melt no matter what you do to it.