Does tofu melt

Assume that 'melt' here is in the same sense that cheese melt, no, Tofu does not melt. This is because cheese contain casein which cause the soft, stringly sticky character of melted cheese and Tofu does not.

This may also be because of the heat damage caused in the tofu making process. Cheese made from cooked milk ( like Ricotta cheese) are crumbly and will not melt just like Tofu which is made from cooked soy.

The closest thing you can get to a 'melted' tofu is finely mashed tofu with nutrition yeast.