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While playing with my Prime to answer the previous question, I found that dividing 10_W by 10_degC gives an error.

In high power electronics this is a very common proportionality equivalent to resistance. typically measured in degC/W (though K/W is also used, and probably more correct)

Knowing this proportionality you can calculate the increase of temperature of a device given the power dissipation.

Can we see about adding this to the units calculations? How about a way to add "proportionalities" as some form of user units?

In this case it is required to use K, so as long as I do that, everything is fine.

It still might be nice to have user defined units along the line of:

ohm = V/A

I was able to enter this ratio as [numerator] / [denominator] > Shift Units Power W / Shift Units Temperature degC Enter. This approach is consistent with the way units generally work, but it does seem a bit awkward or round-about.
If I try to divide the two individual unit objects like you, then I see the same error.