The temperature at which a fat begins to break down and burn is called the Smoking Point. Different fats and oils will have different smoking points. The refinement levels of different fats also play a role in determining the smoking point.
The smoking point will be much lower than what is called the flash point when fats or oils can catch fire if there was a fire source nearby. It is important when cooking that you pay attention to the smoking point of whichever oil you are cooking with and ensure that it does not go too high.