I don't like your theory, Ken.
When the PJ is powered, the fan removes excess ambient heat from the bulb enclosure, but I doubt it actually lowers the temperature of the bulb glass directly. Sure, if the bulb were on without the fan, then the hot air build-up in the confined space would contribute to a hotter bulb and might actually melt the enclosure.
I think a point we can all agree on is that the less heat a bulb experiences, the longer it will last -- more heat means more entropy means more rapid decay of the filament.
JohnK, sure, when the power cuts out, the heat of the entire system will begin to diminish; however, because it's the total heat over time that determines the longevity of a bulb (absent other forces such as vibration shock), active cooling of a recently extinguished bulb will contribute cumulatively to its longevity.
