It's certainly not true that X of Y always means the same thing as Y X. That can be true in certain situations, but most definitely not all the time. Here's an example where it's true:
He is an employee of Microsoft.
He is a Microsoft employee.
One simple counterexample to show that the statement X of Y means the same thing as Y X is not true is that a bottle of beer does not mean the same thing as a beer bottle. The first example talks about a bottle that literally has beer in it (the actual liquid). In the second example, we're talking about a bottle that is used or has been used as a container to store beer as opposed to storing some other type of liquid such as milk or juice. For example, when you go outside and see a bunch of empty bottles scattered on the ground, you'd say that I see beer bottles lying on the ground. You would not say I see bottles of beer lying on the ground because that would imply that the bottles are still full of beer.
Now, let's get back to your "heat button" example. The phrase button of heat actually sounds like you have a button that's made of heat or contains heat, which is kind of nonsensical. The phrase heat button is fine because the word heat is used as an adjective describing the button. What kind of button? A heat button. A button that's probably used to regulate the amount of heat generated in or by some sort of device.