Autoresonance (AR) cooling of a bunch of ions oscillating inside an electrostatic ion beam trap is demonstrated for the first time. The relatively wide initial longitudinal velocity distribution is reduced by at least an order of magnitude using AR acceleration and ramping forces. The hot ions escaping the bunch are not lost from the system but continue to oscillate in the trap outside of the bunch and may be further cooled by successive AR processes. Ion-ion collisions inside the bunch close to the turning points in the trap's mirrors contribute to the thermalization of the ions. This cooling method can be applied to any mass and any charge.