Ok, this looks like a dumb question or even near trolling, but I really don't understand it.

When air is heated over an oven plate, it rises. Obviously, I can check by blowing some smoke in.

The common explanation is that hot air has less density than cold air, and consequently, it raises.

Fair enough, the hot air will end above the cold air, but why is it raising in a column?

With the same argument, I could deduce (and I know that it's wrong) that the cold air above is denser, so it will go down, pressing the hot air away sideways.

What additional fact am I (and the common explanation) missing?

(I'm pretty sure that the tags I found are not optimal.)