A quick search on the net will tell you that cooking butter is not recommended. Indeed, butter that smoke and blackens is responsible for the formation of toxic compounds when cooked at high temperatures. If you have no other fats available, then prefer a gentle cooking. It will take longer but moderate heat will reduce its harmfulness.
The Culinary Academy of Quebec offers a solution on his site: a butter cooking does not burn and does not blacken. In fact, it is clarified butter, what most chefs use for cooking at high temperatures. Ghee butter which comes from milk solids and water were removed. It supports a baking at 252 C, unlike the table butter, which reaches its baking at 177 C.