Hot Hot Heat

The correct answer is before the flame touches the balloon . Before I get to the solution, I'd like to thank @Ram Mohith , who inspired this Brilliant experiment!

First, let's take a look at the full video:

We can all see that the balloon pops well before I bring the lighter's flame in contact with the balloon. Why is this?

Short answer

A flame releases most of its heat into the environment through convection , the movement of heat energy through air currents. Since hot air expands and becomes less dense, it rises above the flame and forms a column of heated air. When this hot column of air sufficiently heats the balloon, it loses integrity and pops.

The longer answer

The flame is hot – a butane-burning lighter produces a flame of about $1400 ^{\circ} C$ . This heat is released into the air around it through a few different mechanisms: anything the flame is touching conducts heat away, movement of hot air near the flame convects heat away, and the hot flame also radiates heat in all directions both as visible yellow-orange light, and as infrared light.

Only one of these mechanisms of heat transfer requires that the flame actually touch the balloon: conduction . Since the molecules in air are so sparsely distributed with large gaps between them, air is a very poor conductor of heat. Until the flame actually touches the balloon, very little heat will be transferred by conduction.

Radiation will transfer heat to the balloon before the flame makes contact. This heat energy is carried mostly by infrared radiation, which travels in all directions equally. The amount of radiation from a flame will be the same two $\si{\centi \meter}$ to the left as it is two $\si{\centi \meter}$ above. I don't recommend doing this yourself, but a flame is much hotter two $\si{\centi \meter}$ above than it is two $\si{\centi \meter}$ to the left. In fact, a flame doesn't feel very warm at all at even short distances to its side, so the dominant method of heat transfer must not be radiation.

Convection is the transfer of heat by the movement of air. As air nearby the flame is heated, it expands. As it expands it becomes less dense than the surrounding air and rises. The cooler air surrounding the flame moves in from the sides to fill the empty space left by the rising air, and is also heated and begins to rise. This process forms a convection column above the flame which carries most of the heat away from the flame.

Don't try this with helium balloons, seriously now.

First lets think about Conduction . Heat is transferred in form of conduction through the vibration of molecules, in this case it is air. As air is a poor conductor of heat and the molecules are loosely held much heat will not be transmitted. Now, come to the case of Radiation . Radiation will occur in whatever medium it may be and in this case to but it will be dominated by conduction because a small source of light will not produce enough radiations to burst up a balloon. Finally, come to Convection . The air above the flame gets heated up and raise up as it becomes lighter. Now the air above will come down and it will get heated up and raises again and this continues. Therefore, more heat will be transmitted in the mode of convection.

1. The flame is brought near the balloon
2. The air in the balloon begins to expand
3. When the expansion of the air is too much for the balloon to hold, the balloon pops

Due to heat of the lighter

There is only one way: try it out for yourself!