The ventilator system and method use a heat exchanger to selectively transfer heat between fresh outside air entering and exhaust air leaving an enclosed space whenever energy can be recovered from the exhaust air by doing so. The system uses a microprocessor-based controller which stores one or more profiles indicating the time-varying needs of the enclosed space for heating and cooling. The transfer of heat between the exhaust and fresh air is reduced or eliminated simply by reducing the speed of or stopping the exhaust air handler while the fresh air handler continues to run. Evaporative cooling for the exhaust air can be provided, and an all-plastic plate type heat exchanger preferably is used, together with an air handler at the exhaust outlet of the heat exchanger to pull exhaust air through the heat exchanger.