Bleaching is a general stress response where the zooxanthallae are expelled. It can be caused by high temperatures, low temperatures, toxins, low light, high light, low flow, infection, or any number of stressors. Any animal housing zooxanthellae can bleach.
You prevent bleaching by avoiding these stressors. Keeping temperatures stable does not help prevent bleaching. In fact, fluctuating temperatures have been shown to prevent the stress that leads to bleaching.