What happened here?

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And I know what you're going to say... that's convection... and it is. But at what point is there no movement in a solid?
The answer is that in a solid there is vibrational motion, but no bulk motion except on a geological time scale. Which is not relevant here. :)

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Before it comes to a boil, why is water hotter at the top than it is at the bottom?

If heat source is at bottom, water at bottom is hotter than at top before it boils. Once it starts boiling, temperature is same throughout water. So the heat source must be at top of water surface.
 
If heat source is at bottom, water at bottom is hotter than at top before it boils. Once it starts boiling, temperature is same throughout water. So the heat source must be at top of water surface.
I posted off the cuff. You are correct if heating the water faster from the bottom than gravity brings the hotter water to the top. My statement was more generalized, heat applied from all directions... ;)
 
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