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Why does it take so long for a gas to reach a thermal equilibrium?

Imagine a 1m cube of air in an insulated container, where you have heated the air in one half but not in the other. Intuitively, given molecules are moving so fast, you would expect the energetic particles from the hot side to distribute themselves throughout the box within milliseconds, equalising the temperature. Why does this instead take much longer?

I thought of this question while waiting for a warm room to cool down after opening a window. Clearly my mental model of temperature is wrong because it seems to me that heat should move through a gas way faster than it actually does.