Besant and Johnson (1995) explain the use of run-around systems during the cooling season.
During the cooling season with ambient air above 18°C (64°F), the run-around system can be used to reduce cooling loads. To take full advantage of the run-around system under warm ambient temperatures it is necessary to cool the exhaust air from about 27°C (81°F) just before it passes through the run-around exhaust coil using an evaporative water spray cooler... . In most dry or moderately dry climates evaporative coolers can reduce the exhaust air temperatures by 5 to 11°C(9 to 20°F) depending on the initial relative humidity of the exhaust air. For buildings in warm, moist climates with high indoor values of relative humidity the temperature reduction of the exhaust air may be only a few degrees and the cooling load savings will be smaller.