Making your own hot air balloon is a good way to experiment with hot air rising. Use a garbage or shopping bag to create the balloon, and fill the bag with hot air using a hair dryer. Turn the hair dryer off and watch the balloon rise. The hot air balloon will continue to float for awhile because the heat will cause the air particles to travel faster and spread apart, which will cause the air inside of the balloon to be less dense than the outside air.
You can determine whether the temperature of the air inside the balloon affects its density or not by making two air balloons -- one with cool air and one with hot air -- and seeing which one rises or stays in flight the longest. Hot air causes a balloon to rise because of the low density of the air inside it, so if the two balloons act differently, you know that hot and cool air have different densities.
To test the relationship between balloon size and flight, use dry cleaning bags and a toaster or popcorn popper as a heating source. To change the balloon size, cut off a few inches of the dry cleaning bag before each launch. This experiment works with the Archimedes' principle, which states that objects immersed within fluids are buoyed by forces that are equal to whatever amount of water the object is displacing when submerged. In hot air balloons, the air around the balloon is the fluid. So the balloon's buoyancy is affected by the weight of the air pushed out of the balloon when the heat causes the air to expand within it.
These experiments can also be done without hair dryers or toasters, which could potentially become hazardous. If you fill two jars with water, one hot and one cold, you can test how balloons react to different temperatures by attaching a balloon to the top of a thin bottle, placing that bottle inside each of the jars and observing what happens to the balloon.