The rubber in tires contains volatile compounds that actually evaporate out over time, making the rubber hard. Heat speeds this process, so yeah, the rafters or attic aren't particularly great places to store tires.
Rubber is also negatively affected by UV light, and by ozone. So you want to keep your tires out of direct sunlight, and away from stuff with big electric motors like washing machines, dryers, large power tools, etc.
Probably the best way to preserve rubber is to wrap it in plastic (to stave off evaporation) and keep it in a cool, dark place. I'd be inclined to put 'em in a closet, wrapped in heavy plastic. If that isn't an option, the crawl space under your house or in a shed that doesn't get direct sunlight might be good choices.
Several years back I bought a '70s vintage Yamaha motorcycle from a guy who kept the bike in his garage. The bike itself was in really great shape, and the tires didn't show any signs of age- no cracks on the sidewalls. But the ride home was the scariest motorcycle ride I've ever had in 30+ years- the 10 year old tires were rock hard and had all of the traction characteristics of kiln-dried oak.