The essence of you project has to do with a property of gas called it's temperature (I know, duh). The best model for an experiment like yours is the ideal gas law. It has many forms, but you'll benefit from the p = MP/RT form. You will also need to talk about what's known as a buoyant force. The net upward buoyant force is given by F = weight of displaced fluid - weight of object is fluid = V(p1)g - V(p2)g.
The phenomenon that causes balloons to rise is a property of buoyancy, which is, in turn, a property of relative density. Density is mass per unit volume, which is effectively the number of molecules per unit volume of air. Density is affected by a number of things, including the type of gas molecule. Gasses like helium are monatomic, and have fewer degrees of freedom (see link). This is why they are less dense than predominantly diatomic gases like air (which is basically nitrogen and oxygen). The specific heat capacity of gasses varies with their relative densities at a standard temperature and pressure (STP). Helium is less dense than air even when they are at the same temperature! It doesn't have to be hot or cold.
In the case of hot air balloons, you are using a property of the gas called thermal expansion to decrease its density. For an ideal gas density is given by:
p = MP/RT
where M is the moles (number of molecules/avagadro's number) of the gas.
As you can observe, increasing T will cause p (the density) to decrease. Decreasing the density of air in a balloon by heating it up will cause it to become buoyant in the surrounding air (which is not heated, and more dense). The buoyant force causes the hot balloon to rise.
Here's the basic principle: if you put an object in a fluid (like water or air) and that object is LESS dense that the fluid it is submerged in, it will tend to accelerate in the direction of decreasing fluid pressure. For fluids here on earth, that's usually upwards. Hence, when we submerge a basketball in a pool and let go, it flies up out of the water. Similarly, a less-dense Helium-filled or hot air balloon rises up towards the low-density upper atmosphere. The Helium balloon is less dense because of its lower specific heat capacity, and the hot air balloon is less dense because of its higher temperature. A hot helium balloon would be the least dense option possible. However, if you want to do an experiment to see how heat affects density, you should use balloons filled with air, then heat the air up.
NOTE: Don't use rubber balloons, as these increase the pressure of the air inside of them because of their elasticity. It is also hard to heat the air inside of a rubber balloon. A different experiment for demonstrating the hot-air principle is using a candle to heat a metal plate. Above the metal plate place a very light pinwheel. The pinwheel will spin when the air beneath it is heated.