The Maxwell-Boltzmann distribution

Temperature is often introduced as "the average kinetic energy of the molecules", and the word doing the quiet work there is average. At any instant a gas contains molecules crawling along and molecules moving several times faster than typical, constantly trading energy through collisions. The Maxwell–Boltzmann distribution is the stable shape that this traffic settles into: a curve rising from zero, peaking near a typical speed, and falling away with a long tail towards high speeds.

Heating the gas does not slide that curve sideways. The peak moves right, but the curve also flattens and the tail stretches, because the distribution must still enclose the same total number of molecules. The consequence matters more than the shape: the number of molecules above any given speed threshold grows far faster than the average speed does. Chemical reactions with an activation barrier speed up dramatically on modest heating for exactly this reason — it is the tail, not the average, that gets over the barrier.

Mass sets the other axis of the story. Thermal equilibrium equalises average kinetic energy, not speed, so at the same temperature a light molecule must move faster than a heavy one. Helium at room temperature has a distribution reaching far higher speeds than nitrogen does, which is why helium leaks through small openings more quickly and why Earth's gravity has retained nitrogen and oxygen while losing almost all of its hydrogen and helium to space.