Does nature prefer high entropy and why is entropy lower at higher temperatures?
Nature's bias is towards an increase in entropy. This is a fundamental law of the universe; there is no reason that can be used to explain why nature prefers high entropy to low entropy. Instead, increasing entropy is itself the basic reason for a wide range of things that happen in the universe. Changes in temperature will lead to changes in entropy. The higher the temperature the more thermal energy the system has; the more thermal energy the system has, the more ways there are to distribute that energy; the more ways there are to distribute that energy, the higher the entropy.
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