Why does hydrogen conduct heat so well?

Hydrogen conducts heat better than any other gas primarily because of its extremely low molecular weight.1

According to the kinetic theory of gases, the thermal conductivity of a gas is inversely related to the square root of its molecular mass. Because hydrogen is the lightest of all gases, its molecules possess a higher velocity than those of any other gas at a given temperature. This high molecular velocity allows kinetic energy to be distributed and transported through the gas more rapidly than in heavier gases. Consequently, hydrogen exhibits the greatest heat conductivity of any gaseous element.21