Nah. Temperature is NOT heat. It is heat divided by mass. A very low-density cloud could be amazingly hot, yet generate very little heat.
Your point is well taken, but incorrectly expressed. 1/2kT is the average energy per degree of freedom. In an ideal gas of point-like particles, the energy is 3/2nkT, since 3-dimensional space affords 3 degrees of freedom for each of the n particles in the gas, independent of their mass. This means that a gas of massive particles in thermal equilibrium with a gas of less massive particles wil have a lower average velocity.
Mark Twain quipped, "That's the wonderful thing about science. One gets such a wholesale return in conjecture on such a trifling investment of fact."
We might put a positive spin on this observation by noting the broad implications of simple fundamental definitions.