Overheating issues when I am stopped in idle

I am having an issue with my car overheating, but it is only doing it when I am stopped in idle, such as at a light or in a fast food drive through or when I am driving at very low speeds like ten mph and only if I am doing any of these things for more than about five to ten minutes. As soon as I take off and drive at regular speeds again it immediately cools back down. But if I just get up and go start the car in my parking lot and just let it run without going out driving, I can sit there for twenty to thirty minutes and it will not overheat. It has a white smoke from the exhaust on cold start and the exhaust has an oil/fuel smell. The smoke does dissipate after a couple minutes. I am burning through coolant quite frequently, but have not found any visible/noticeable leaks. There are no signs of oil in the coolant or coolant in the oil. I am stuck not knowing what the exact problem may be. I know all the possibilities, but cannot figure out which one it is.