According to the USDA, it's best to store food at temperatures below 85 °F. Many of us won’t see 85° consistently until October. High temperatures (over 100 °F) are actually harmful to canned goods. The longer items are exposed, the more harm done. “Harm” ranges from nutrient loss and a change in appearance for food in glass containers to bacterial growth.
Different bacteria grow at temperatures from 32°F to 158°F, with bacteria causing foodborne illness growing best at body temperature. Whether that means temperatures around 98.6°F are most problematic, I don’t know. I’m not a scientist. Nor do I know the calculus for temperature change over time at a certain heat. (I do know my enchilada casserole heats through in 30 minutes at 350° and a pork loin takes longer.)
On this topic generally, Google wasn’t particularly helpful. (Its first two hits were from bloggers, “beprepared” and “survivalmom.”) But what does seem certain is cans and glass containers are most susceptible to spoilage from exposure to oxygen, not heat. Extreme temperatures cause container expansion and contraction, compromising seals.
Maybe the best notice to post at our projects is notice about discarding items that are deeply dented, bulging, leaking, or heavily rusted.