I'd be surprised if the cause was the temperature from the information on their website. Peregrine chicks can't thermoregulate so the parents are in charge of temperature control for the first week, ten days anyway. And they do know how to keep their chicks warm/cool/dry. Warmer is actually easier for them to do, basically they sit on them, which is what they are doing anyway right after hatching. That all three chicks should have died so quickly in the first couple of days, would make me suspicious. The fourth egg with a hole isn't enough information for me to speculate upon. Don't get me wrong, it could have been the temperature, don't know enough about the site, the adults or the weather the days in question. But like Taku last year, the deaths seems so out of character. It will be very interesting to find out what happened there, hope they do/are able to post the results when they get them.