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Totally an elementary question.
Staring at a candle, it appears that the bottom of the wick is dark whereas the top glows. However the bottom of the flame (the blue) is the hottest.
Is the reason for this that the concentration of liquid wax is greater at the bottom, offsetting the greater temperature at the bottom?
The wick temperature does not have to be the same as the flame temperature.The flame is hottest at the bottom, but the wick is hottest at the top.
For a candle, the wick burning isn't the intended purpose of the wick; light comes from burning wax (more generally: fuel), you want to burn the wax not the wick. Rather the purpose of a wick is to help fuel evaporate by soaking up wax and allowing the radiant energy from the flame to heat the wax causing it to evaporate and burn also.
As wax travels up the wick, it evaporates and less wax is in the wick the further up you go. Eventually the wax dries up and the radiant energy is heating a wick without any wax. Eventually the wick gets so hot at the tip, that it will glow due to black-body radiation.
In summary: though the blue is the hottest part of the flame, the wick can evaporate wax to cool towards the bottom. There is no wax at the top and thus as the radiant energy of the flame causes it to get hotter until it starts to glow.
Extra: I will note that the top of the wick does not burn when lit as the gas around the wick has too little oxygen to burn (unless the wick slumps out side the flame). When you blow out the candle the low oxygen environment of a flame is gone and thus the hot wick will smoulder.
Because fire is not the same thing as light.
Michael Faraday did a wonderful job of explaining how the candle works, and I direct you to look at it (there are also Youtube videos giving a modern take on this work) if you're interested.
In short, the candle produces light, not because it is hot, but because it is sooty. The particles of soot glow when they are hot (blackbody radiation), and that's what produces light.
If you take a flame where the fuel is very well-mixed with oxygen and the flame that's produced is not sooty, it does not glow like a candle even though it's very hot. This is precisely why Bunsen burners are used in a laboratory. They give a hot but non-illuminating flame that's great for doing analysis.
