Answer
The air inside a balloon is a poor conductor of heat, so the rubber of the balloon skin absorbs most of the heat without the possibility of passing a great deal of it on via conduction. The heat gets conducted to the air inside, which has a low heat capacity, and warms quickly. A rise in temperature of the rubber causes a breakdown in molecular bonds and the balloon bursts.
When filled with water, the balloon has water, which is a good heat conductor and
has a large heat capacity (it can take large amounts of heat with low change in temperature). In this case, the rubber passes on the heat to the water, whose temperature does not rise extremely, keeping the skin of the balloon intact.
Work Step by Step
Given above.