Depending on the ripple current, the capacitor will self heat and could be hotter than the surrounding air.
Semiman
Agreed. I didn't say it didn't generate ANY heat. And, this is all the better reason to actually measure the case temperature of the cap itself, especially if someone is asserting it's the weak link in the reliability chain...
Also, as I think this over, before we go second-guessing the Cree design, we ought to consider that electrolytic "life" ratings are a function of many factors, none of which are known. For example, I see they chose a 315V cap, but don't know the applied DC voltage. If its less than 315, then life increases. Also, we don't know to what degree the capacitance or ESR can drift out-of spec (technically, a capacitor 'failure') but still allow the lamp to operate normally. IOW, we don't know how much margin was used in the design.
Lastly, Cree's guarantee of 25k hours stands irregardless of what we might think of their design choices. They are not guaranteeing any particular lamp will last 25k hours. Rather, they are simply agreeing to replace those that don't.
Yes, in case it wasn't apparent, I get annoyed when I hear something like "the lamp runs hot and therefore the service life of the capacitor is questionable - design error?". That is an oversimplification, with possible bias, of a complex subject...