An oil with a high smoke point (the temperature at which oil starts to smoke and burn) like peanut oil, which has a smoke point of 450 degrees, works best in a turkey fryer. Most recipes call for frying a turkey at 350 degrees so that high smoke point provides plenty of room for error. Corn oil, although less flavorful than peanut oil, has a high smoke point and is safe for people with peanut allergies. Canola oil can work only if you watch the temperature, as it smokes at 400 degrees. Olive oil, with a 320-degree smoke point, makes a very poor choice.