I fitted a pair of Schwalbe Big Apples that had been standing in their boxes on top of a bookcase in my study for 9 years, out of direct sunlight. No problemo. I'm inclined to agree with Steve et al that the killer is UV.
I don't know about heat. I keep used but still serviceable tyres (taken off to force service items to coincide with gearbox oil changes) in a ventilated cupboard in the laundry, which is heated and suffers from varying temperatures because it leads outside and the doors are always opening and closing and the machines put out heat on top of the central heating when operated: again, no problem, nor on the tyres in the loft, which likely suffers extremes (such as they are in Ireland) of temperature but doesn't get much sunshine.
As point of information only, given without ascribing significance to it: the used tyres downstairs are in a cupboard with louvred doors and thus good air circulation. Even the tyres in their own boxes on top of my shelf have some sort of circulation, and the ones in loft have excellent ventilation because there are several windows slightly open year round to circulate air in the house. I mention this only because others have made a point of sealing or semi-sealing their tyres against light, and coincidentally may cut off air circulation.