The ambiant temperature definitely matters, I agree that even in a much cooler room it will get to an unacceptable temperature though.The ambient temp being 80F is arguably irrelevant to the heat of the UTH. If you really want to argue that it makes a difference, I will attempt this same experiment again in a 65-70F room. I am fairly certain that the UTH will still reach 110+.
But at the same time a lot of cases where somebody is using an unregulated UTH, they also have a heat lamp increasing the local temperatures as well.