I doubt if your ball would damage your friend's alley.
Any damage to your ball will be obvious when you take it out of storage, and I doubt if there will be any. What happens up here in CT is that bowlers take their ball from the nice warm bowling center and then put it in the ice cold trunk of their car until the next week when they take it out to find a nice big crack in it. In mini-storage the temperature change should be much slower. the only effect may be that the 100+ degree days may have pulled some oil from the ball which would be a good thing.
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