I (personally) would not page in the middle of the night for a temperature issue. The systems should be resilient enough to handle some cpu throttling. A non-transient issue like this would probably end up in a ticket queue.

In a huge system with lots of failover you won't notice all the contingencies they identified planed for and successfully mitigated. Then something breaks which; you thought would be covered under another redundancy, was covered until a recent change (firmware change to the HVAC system), you didn't plan for etc...

And everyone points at the failure and says "that seems obvious", meanwhile the mountain of tests and monitoring and redundancy goes unnoticed.