I'm not a scientist, but I'll do my best to figure this out.
Temperature is basically an aggregate measurement of kinetic energy, because we can't get the energy of each individual particle, we get an average.
Since the current in lightning is actually not very large, and even smaller after it goes through the resistor that is your body, there probably aren't that many electrons actually passing through you. Now, each of those is carrying a HUGE ammount of energy, but the current is what we want to look at.
So we have some of the lightest particles in the world, electrons, passing through the gun. And there aren't many of them. That means that the total kinetic energy passing through the gun is probably not very high. Ergo, not much heat. Besides, the gun itself is a conductor, a much better conductor than either you or the air around you. Low resistance means no molecular collisions, which means minimal energy transfer, which minimizes the heat that appears.
I think what is written down as the heat of lightning is actually the heat that appears in the air as the electricity passes through it. That would happen because the resistance of air is extremely high, so high in fact that most books just assume it to be infinite for the purposes of electrical wiring.
Conclusion: You are probably safe from lightning in the gun because the gun won't heat up much. Now what it does to your body is a different story. It's survivable, but you'll definitely lose some movement.