I have a 1995 Avalon with 181,000 miles on it. It started doing this at about 170,000 miles and it's now in for service to have all new gaskets and seals. I had three mechanics look at it and all of them said a gasket/seal was leaking oil into the cylinder heads. They said the smoke is the oil burning out of the cylinders. All of them said it doesn't hurt the engine, but did require me to add about two quarts of oil per month.
I'm only getting it fixed because it was getting a bit embarrasing. The bad news is that, at least on the Avalon, this is an expensive fix.
Mine would usually only do it if it has sitting for more than about 3 hours. Strange thing was that it didn't always do it.
By the way, I tried a LOT of different oil weights and additives...nothing worked.