As you suspect, the real risk is the heat. Nearly all bottled water contains little critters inside that can thrive in and spoil water above 120 degrees F.
Also, as ras stated, many cheaper polyethylene plastic bottles will react under heat like that and foul the water--thicker polycarbonates (think canteen plastic) will hold up much better.
And as deputy tom writes, look for and abide by the expiration date. If no expiration date, assume 6 months provided the water has not been exposed to the air since bottling (in other words, if you reuse the same bottle, you're exposing the water to air).
So-called "pure" bottled waters will last for 12 months or more--but look for a date.