What will happen? Will that end start boiling before the other end a mile away? Or is the heat transfer basically instantaneous and the temperature rises uniformly throughout?

If it does boil and create steam, what does the middle of the tube look like? A mix between gas and liquid? A smooth transition between the two?

And what would happen at the other end? Cold water with a shit-ton of pressure because the steam on the hot end is expanding?

Finally, if there is non-uniform temperature rise, at what scales is it noticeable - actual water on one end and actual steam on the other. I chose a mile because it seemed extreme. But maybe it has to be 100 miles before it becomes noticeable. Maybe it can be less. What is the minimum length?