The law of convection being ... what, that the hot stuff rises? Then, sure, that will always continue to apply.
This does sound like a good homework question, ybhathena, so maybe I shouldn't say too much. It might be for you to think through.
On a practical level, in the lab have you tried heating a test-tube containing liquid (e.g., water) from the side? (Over a Bunsen flame, of course.) [/color]
What lesson did you learn from that? Can you explain it?