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.
Gen 6:20 reads as follows in the KJV:
Of fowls after their kind, and of cattle after their kind, of every creeping thing of the earth after his kind, two of every sort shall come unto thee, to keep them alive.
The sense here is that the animals came to Noah, not that Noah went out and got each animal. I'm not sure that if I were a polar bear, I'd want to walk all the way from the polar regions to the ark, but if God is compelling the animals to come, then come they would have.
Also, remember that Noah had been building the ark for 100 years before the flood began, so there was ample time for the animals to reach the ark.
There are two issues with your question. First, the assumption the polar bears must have been on the ark. The Bible specifies that there were two of each "kind". If we take this to mean two of every species that modern science defines, then that would necessitate many more animals on the ark. If, however, it just means that there were two of each kind, then there would be much fewer animals on the ark.
The idea is that all the genetic information for domestic dogs as well as coyotes (and perhaps wolves) could be contained within two representative wild dogs at the time. Indeed, we can expose the range of variations in domestic dogs to get Great Danes and Teacup Poodles.
So, if there were two bears that contained sufficient genetic information to account for the various species we see today, black, brown, polar, grizzly, etc., then polar bears need not be on the ark, except within the genetic makeup of the two bears that were selected (probably very young bears--one pink and one blue).
The other assumption is that the pre-flood climate is basically what we have today as well. There is sufficient evidence to show that this assumption is probably false. For example, we find wooly mammoths eating tropical vegetation in what are now arctic regions.
Biblically speaking, people lived far longer prior to the flood than they did afterward. A drastically different climate could certainly account for this.
So, Noah probably took one of each "kind" rather than one of each of the isolated species we see today. Noah had 8 people--not 2 Chinese, 2 Europeans, 2 Africans, 2 Native Americans, 2 Computer Programmers, etc. Also, the climate was likely much different then than it is now.
Let's address this question for the different views which are common about the Flood:
The description of the Flood is to be taken literally, word for word, as a depiction of real historical events about a global Flood. In this case, it's a miracle. A global Flood which covers all the mountains of the Earth can not happen naturally, there is not enough water for that on the planet, so it was a miracle. In case of a miracle, nothing is impossible, and the acquisition of penguins and polar bears is dwarfed by much stronger "violations of the laws of nature how we unterstand them".
The description of the Flood is to be taken literally, word for word, as a depiction of real historical events about a local Flood. In this view, the "whole world" actually means the whole world known to the people of that time. In this case, there is no need for penguins and polar bears, as they were outside of the areas affected by the Flood.
The description of the Flood is largely symbolic. Just as in point 2., there is no need for penguins or polar bears here.
Couldn't the answer simply be: "God 'snapped his fingers' and there they were." Because that is how other non-natural events' origins are often attributed in Christian traditions (e.g., the Red Sea parting, the burning bush, virgin birth...or, well, the creation of the entire universe). If God is taken to be omnipotent, what is the point of thinking anything mentioned in the Bible is, in your word, "implausible".
This is an answer for any implausibility you could find with this story (or any others). Not enough room on the ark? SNAP! Sure there is--it's like the TARDIS. Etc.
I have trouble understanding why, if one believes in the existence of an omnipotent being, one is later stymied by "challenges" he and his followers might face.
One school of thought on the flood holds that it was not in fact global, but just occurred in Mesopotamia. The argument is that Psalm 104 indicates the earth would never be fully covered with water after the creation, and the Hebrew words for "whole earth" in the flood account generally indicated a local area. So Noah only had to save "local" animals, which, presumably, did not include penguins and polar bears.
The flood was global, otherwise God most probably wouldn't have instructed Noah to build such a big vessel to accommodate just the regional animals and birds.
Ice floats on water, so the flood wouldn't affect animals and birds that live on ice.
More than 50% (or likely, more than 75%) of the animal kingdom including fish lives on water; then there is another percentage that are amphibians, all of which wouldn't be affected by the flood.