Why does a hot air balloon rise when it ls heated?
Basically you can see it through Archimede's Principle.
Because the density of hot air inside will be lower than that of the air outside and, from Archimede's principle, the baloon will receive a lift upwards or buoyant force that is bigger than the weight of the baloon causing it to rise.
From Archimede's Principle the baloon receives an upwards force equal to the weight of the displaced fluid (air). In this case the displaced air is denser than the air inside that, so, weigths less because less dense; the baloon will rise because of this force that will be greater than the weight of the baloon (and of the rubber of the baloon) and so it will tend to make the baloon to go up.
If the air inside were at the same temperature of the outside air, the lifting force and the weight of the air inside the baloon would be the same....but....the baloon would drop because of the additional weight of the rubber of the baloon!
Hope i didn't confuse you even more!