Yeah Peter, but the bulb is hotter when the projector is on(with the fan running of course)than it is during the few minutes of the extended cooling period with the fan off after an occasional power failure. So there's less additional heat involved than if the projector was simply operated normally for a few more minutes(i.e., if the power hadn't failed). The previous point still applies; there's no damage done to the bulb by a power failure and no need for a UPS in the situation.

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Enjoy the music, not the equipment.