Because if there is no heater, and the air is turned off or turned on during the day, it could cause the fish to get stressed out, which is the main cause of fish getting Ich. ( I can only assume that is what the fish has). In nature the water on a shallow reef changes several degrees, possibly 5 or more degrees a day, from coolest in early morning to warmest at late afternoon, but it is slow. In a small tank it can change quite fast, too fast for some fish. I had a tank that during a water change in the winter, I had a heater in a corner , and unplugged it. I forgot to plug it back in and the next morning a female gold striped maroon clown had ich. I plugged the heater back in and it went away. I did it again about 5 years later, same problem, same fish. She went on to lay 1000s of eggs and have many offspring, and now is Brian Greenes and has bred for him too. That was 13 years ago, and she is still alive, along with her younger mate. And she was full grown at that time. But a heater could definetly be the culprit reason of Ich. Remember what ever stresses a fish out bad, will cause Ich to manifest. Water cleanliness, is a big stressor. The quarentine tank will certainly fix the ich problem, especially if meds are used, but put the fish back in a stressful condition, and it will happen again. If the fish dont have a stressful life, and clean water, proper temp range, fed enough, they should never have ich.
