It takes a lot of heat, usually in cycles of hot-cold-hot-cold, amd lots of humidity in similar cycles, to have a significant effect. Folks are buying surplus ammo all the time and seem to have no problems with it. Some issues you might see are oxidizing of unjacketed lead - if nothing else it's horribly abrasive. And if you believer that military ammo storage warehouses are climate-controlled I'd like to talk with you about my oceanside property in Arizona - I'll let it go at a good price.
The old canard about the box of ammo in your trunk for a few years being no good was probably started by a gun store clerk who got a commission for every box of ammo he sold.
Now, if you were storing your ammo in water or in oil you might see deterioration fairly quickly.