Fluctuating temperature is an enemy of food. It's simply not the best thing to do to store it in such conditions.
That doesn't mean it won't be inedible--MikeK tells of his experience eating food that was in an outside storage locker years after it was put away--just that if you can avoid doing so, avoid doing so.
If your garage is attached to your house, a way that could dampen the temperature swings is to install a cabinet to the wall on the heated side of the garage, make it tight and sealed to the wall, then make the cabinet seal as well. It will pull some heat from the house (and cool too, in the summer), which will dampen the temp swings. It'll work even better if you can insulate it somewhat, perhaps with foilboard.
And FWIW: When we built my house, I insulated the garage, much to the amazement of people who saw me do it. Well, I live in Wisconsin where the temps can reach the high 90s in summer, and -20s in winter, and that garage virtually never drops below freezing in the winter. Not only does it "borrow" heat from the house (it's an attached garage), but the heat from the cars in the winter warms the garage!
I test the warmth by leaving a small glass of water on my workbench to see if it will freeze, and it doesn't.