A first-order model is developed for collisional activation as effected via resonance excitation and helium buffer gas in the Paul ion trap. For an ion population at steady-state under specified experimental conditions, the kinetic theory of ion transport in gases is first used to calculate an effective temperature shown to be identical to the internal temperature for molecular ions in an atomic gas. The evolution of the ion internal energy is then followed by a random walk simulation designed to be representative of the actual collisional energy transfer process, except ion losses due to dissociation and reactive processes during collisional activation are excluded. During the simulation, inelastic ion-neutral collisions increase the average ion internal energy via small energy changes (both positive and negative) until a steady-state condition is reached in which excitation and deexcitation processes are balanced. Histogramming the simulated data reveals a Boltzmann-type internal energy distribution whose average internal energy is the same as that calculated for a true Boltzmann distribution at the same internal temperature.