Where did Noah find polar bears and penguins in Palestine? The biblical account of Noah's Ark and the flood seems implausible to me due to this detail. How could animals accustomed to thriving in extreme temperatures be found in a common place for preservation aboard the ark?
First of all I live in the Middle East in the same country as Mt. Ararat where the ark landed. Note this is not in Palestine nor do we know where Noah started from. The problem could just as well have been that he was starting from the Siberian tundra and needed some African wildebeests. You're trying to solve a specific problem that you don't have enough scenario data to build a case for or against.

However back to the plausibility argument. Here in the neighborhood of Mt Ararat there is a zoo here that has penguins. They are kept out of doors and, with the exception of having free access to a small pond, cope with the same baking heat the rest of us deal with. They may not like it but they survive.

Secondly I grew up in the Southwest high desert. The zoo where I grew up had a polar bear exhibit, again out of doors. In more recent years it has acquired some shade and a larger (very fun looking) series of pools but the one I remember as a kid wasn't much more than a concrete box.

As if that wasn't enough to at least cast doubt on the argument against the plausibility of such a thing, let's consider the other implications of the flood.

Hand in hand with the flood come a host of other radical global changes. The arrangement of dry land vs ocean has likely radically changed as tectonic plates rose and fell in order for the water to cover the whole land. How high mountains were, where they were located and even the divides between contents are likely very different.

In the same vein, global climate would have been radically different. Many believe from the Genesis account that there were changes in the atmosphere and that likely post-flood earth has a lot more extremes of hot and cold in different areas than pre-flood earth.

Lastly, it's not always alleged that every variation of species we have today was on the Ark. It's possible a representative of the bear family was all that God required to cover the basis for both polar bears and black bears.

And most importantly, don't you think the God who created the animals in the first place and gives them the instincts that make them what they are could not manipulate the system in a miraculous way to lead a couple of stray bears on a long walk? Similar wild and seemingly impossible journeys by strangely motivated animals have been documented

All in all, the specific allegations you bring up are small items in the big picture. If you really have a problem with the science, you need to start at the other end of the spectrum and work backwards. Those little details sort themselves out in the big picture.