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A friend once noted that the temperature had doubled from morning to afternoon, from 42 degrees to 84 (Fahrenheit; this was in the U.S.).

I didn't contradict her, but thought to myself that wasn't really true, because the actual doubling of 42 degrees would be the span from absolute zero to 42 multiplied by 2. So for the temperature to double, we would have to have long before that burned to a crisp.

Since "0" is a seemingly random "starting point," it really shouldn't figure into a calculation of when a temperature has doubled, correct?

But we do, of course, say that if you get a raise from \$22 per hour to \$44 per hour, your salary has doubled. Because 0 is a solid basis from which to begin.

Are my assumptions valid?

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    I think this is more physics than math, but: the temperature *difference* was the one doubled, and not the temperature itself. – 2017-01-07
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    @J.M.isn'tamathematician: the only difference that has doubled is that between the ambient temperature and $0^\circ$ Fahrenheit. The OP is asking, what's so special about $0^\circ$ Fahrenheit? And the OP is right to wonder. – 2017-01-07
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    Then, "what's so special about 0° F?" puts this question squarely in the physical realm and not the mathematical one, @Tony. I'm sure you know of how Gabriel Fahrenheit started from brine to construct his scale. – 2017-01-07
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    $42$ is the answer – 2017-01-07

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The only thing that makes sense in this context is the absolute zero. That's also what makes, for instance, the ideal gas law look the nicest (temperature doubles and volume stays the same means the pressure doubles, and so on). That means that twice as warm as the temperature at which water freezes turns out to be about $273^\circ C$, or $524^\circ F$.

You get more or less the same thing happening with altitudes. Height above sea level is kindof arbitrary, and doesn't actually correspond to actual height above sea level most of the time because of wind and tides. And in the middle of a continent, what is sea level, really? So if you have two mountains, and say that one is twice as tall as the other, does that make sense in any objective manner?

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    Please stop editing in mistakes in my answer. – 2017-01-07
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    N.B. $273.15 K$ is "cold"; $273.15 {}^\circ C$ is "hotter than boling". Also you botched the conversion; 491.67 Rankine is the freezing point of water. – 2017-01-07
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    @J.M.isn'tamathematician The temperature _twice as warm_ as the freezing point of water. Read more thoroughly next time, please. – 2017-01-07
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    Okay, and where was the $524$ obtained, if so? – 2017-01-07
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    @J.M.isn'tamathematician Converted from $273.15^\circ C$, the same way one _always_ converts between Celsius and Farenheit degrees: using google. – 2017-01-07
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    Ah, I forgot the additional term of $32$. Thanks for your patience. – 2017-01-07
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    @J.M.isn'tamathematician Next time you're uncertain about something like this in an answer or a question, ask about it in a comment instead. That way you don't interrupt edits like you did to me now (I was almost done with the altitude addition the first time you did it, and it disappeared). – 2017-01-07
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    I once knew a man who froze himself to absolute zero. He was $0K$. – 2018-01-01
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Considering human sensation, I would take for the zero a point such that we don't feel warm nor cold. According to standards, a comfort temperature is like $24.6°$C, or $76.28°F$. Then the initial $42°F$ is just... pretty cold.