[T77911S]

nothing gets hot enough on the oil tank to create smoke. oil on the exhaust makes that kind of smoke.
you need to look under the car for a nice big oil leak that makes that amount of smoke non stop. that is if keeps smokes like that continuously.

when first reading your post I was thinking a small amount that could possible be coming from the engine and blow by making its way back into the oil tank and out, perhaps the oil cap as someone suggested or maybe from a hose connections on the tank. buts that's a lot of smoke.