How to get the first step of the derivation of the Maxwell-Boltzmann distribution
KT comes in from requiring agreement with the ideal gas law.  

See "section 1.5.3 $\langle v^2\rangle$ should agree with the ideal gas law" and section 1.3 "The functional form of the dependence of T on $\langle\varepsilon\rangle$ cannot be determined solely from kinetic theory, since the temperature scale may be chosen in many possible ways. In fact, one way to define the temperature is through the ideal gas law: T = pV/(nR)" in Kinetic Theory of Gasses