I am just a recreational rum drinker, not a professional so this is just my observation.
While Rums are not sensitive to the point wine are, I have found that when a rum is left in fluctuating heating and cooling for a while (like when I forgot that I had stashed a bottle of Eldorado 12 in the shop in the winter only to find it in August
) they lose their edge. I can't quite put a name to it, but that bottle doesn't taste the same as my liquor cabinet bottle. I have however gone so far as to put my bottles of Appleton 30 year in the wine cellar for constant temperature control. I can't say that the cool helps, but the constant temperature couldn't hurt.
I would love to hear an experts answer on this.