This is an interesting problem - biologists have been interested in finding explanations for the worldwide distribution of many groups of organisms for over a century and a half.
I agree in part with what Kaysie and Alex said. Physiological limits probably do provide part of the reason for why salamanders do not occur in some parts of the world.
However, temperature alone cannot explain the worldwide distribution of salamanders. For instance, not all plethodontids in the tropics have a high-elevation distribution.
The other thing to consider is the biogeographic history of salamanders: where and when did salamanders originate, and what did the world look like then?
The best fossil evidence indicates that most modern salamanders arose about 160-170 million years ago, in what is now Asia (sirenids are an exception). At that time, Asia, Europe and North America formed one big continent "Laurasia" that was separating from the other big continent "Gondwanaland".
Thus, salamanders have been evolving in Asia, Europe and N. America for the last 160 million years, at least.
Gondwanaland included what is now Africa, South America, Australia, India, and Antarctica. Salamanders never had the opportunity to live in Australia, and only recently (geologically speaking) have had the opportunity to move into and evolve in Africa and South America.
However, the potential for salamanders to evolve into and survive in tropical environments is clearly shown by the plethodontids that exist in tropical central and South America, including the Amazon Basin, Yucatan pennisula and other low-elevation sites.
Mike