A question about Noah's Ark...?

We are told that Noah built an ark and had two of every species of animal onboard that arch for 100-days. How did Noah manage this, considering he would have had to have a climate that accounted for Polar Bears that require the ambient temperature to be below -2C, and Amazonian tree frogs that require the ambient temperature to be +30C. Also -- given that all other life was exterminated by the floods that Noah's arch supposedly protects the animals from, how did the population of the worlds animals recover considering that they were the product of such a limited gene pool. There would not be enough genetic diversity to produce a sustainable blood line, considering that from one breeding pair of crocodiles (for example) every other crocodile that has ever existed are direct decendants (mother breeding with son, daughter breeding with father, sibling with sibling, etc.).