Hot Air

I saw an interesting display at the "Magic School Bus" exhibit at the Discovery Museum in Sausalito I'm wondering about.  It has four silvery balloons with heaters under them.  When you press a button and heat up the balloons for several seconds, they start to rise up in the air.  The exhibit explains that the heating speeds up the air molecules inside the balloons and makes them hit each other harder and further apart, so they weigh less, causing them to rise.  But watching the balloons closely, I cannot detect any expansion of the balloons at all; the hot balloons look exactly the same from the outside as the cold ones.  I had always imagined hot air to be less dense than cold air and therefore to occupy more volume, and this to be the reason hot air rises, but is this correct?  Is relative density the cause, or is hot air simply lighter, intrinsically, than cold air?  If the hot balloons occupy exactly the same space as the cold ones, I don't see why they should be lighter and should rise.  Sidney Keith