Is it smoke or steam? Is there a sweet smell to it? If it is steam and smells sweet, then you are getting coolant into the combustion chamber, meaning you have a head or head gasket problem. Starting it, letting it run for a few minutes, and shutting it off could cause a head gasket to fail. What you are doing is putting the engine through a quick heat cycle. When the parts heat up and cool down, they expand and contract and different rates, thus causing a head gasket to fail.
If the exhaust does not smell sweet, then it could be oil burning. However, smoke from burning oil has a blue tint to it. This could be caused by many different things such as bad rings, bad vavle guides, ect.
