Overheating can cause damage to a laptop's LCD screen, but if everything is working properly, it shouldn't be an issue. For temperatures to be the cause of the crack, it would have to be overheating and then suddenly exposed to extreme cold. If it heated up enough to break the screen, you would see a burn mark on the display. It may have heated up and, while in your bag, it was somehow hit or increased pressure and cracked.
No, it will not be covered by warranty as allowing the computer to overheat to that extent is negligence on the user's part. You can take it to Apple and, if there is a known problem with that model's screen, a replacement recall may still be in effect. Otherwise, you'll have to pay for repairs. They won't give you a new computer.
Yes, glass can break even at room temperature. First of all, it's not the user's fault that there is a crack in the screen and it's quite obvious that it wasn't caused by a fall; otherwise, the screen would have broken and wouldn't have a diagonal crack. My second screen now broke under exactly the same circumstances; I left my laptop in the kitchen overnight, 100% sure that there were no cracks before, and I woke up this morning with a huge crack in the screen. I've Googled the causes of the screen cracking and the most common reason is that the laptop overheats and the screen cracks.
I've already asked on the Internet and I've heard that the only thing that can cause a laptop screen to break is a sudden change in temperature.