There are two possibilities to make the balloon take off:

1st possibility: You decrease the weight force

You use some kind of gas with the same volume as air but which is lighter, thus its density is smaller. Consequently the weight force of the balloon decreases and the lifting force makes it take off:

2nd possibility: You increase buoyancy

If you heat air or other gases, they will expand. So they achieve a greater volume. The mass and thus the weight force do not change. Due to the fact that the volume is greater now, more cold gas is displaced. As a result buoyancy will increase: