It's a bad situation, I'll give you that. But yes, the dry heat most likely had a bad effect on the ball. It also depends on the temperature, how fast it heats up to that temp and then how fast it cools down. Super glue IS an issue because it expands and contracts at a different rate than the ball does, but only if a significant amount is used.
It's impossible to know exactly what caused it, but if it wasn't cracked before, something was done to it, and then it cracked, it's really easy to point a finger, and really hard to convince someone otherwise when it appears to be that obvious. You might give them a discount on a new ball, but just like cars and insurance, if someone causes a wreck with you, their insurance only has to pay the value of the car, not the brand new value. So IF you're even responsible in the first place, I don't think you're responsible for delivering a brand new ball. Either the amount of a discount for the estimated value of the ball, or a used ball of equal value, etc.
That all being said, I'm still not convinced it's your fault. An old ball could crack at any time for a variety of reasons, but in your situation if you're trying to do your best to "make it good," whether it's your fault or not, I still don't think your offer or compensation should be any more than whatever value you estimate that ball at. That's both fair and reasonable.
