The more complicated nerdy method starts with equality of mass of extract (wex):

wex = d15 * SG15 * P * V15 = d20 * SG20 * P * V20

where

d15 = density of water at 15C

V15 = volume of wort at 15C

SG 15 = specific gravity of wort at 15C = SG(15/15)

etc.

Then a little algebra gives

SG20 = d15/d20 * SG15 * V15/V20

To get the volume ratio I could use the cubic coefficient of expansion for water (k) (or better yet for wort). And this the first problem - for water at 20C k = 2.07E-4; at 15C k=1.51E-4

Anyway,substituting the volume ratio with V15/V20 = exp(k*(20-15)) ought to give me an answer for SG(20/20). Except (1) I can't find any SG(15/15) and SG(20/20) for the same Plato and (2) k is clearly not even close to constant which is important since the none of the multiplicative factors in the SG20 equation are very far from 1.

I also thought perhaps if there were reliable SG20 and SG15 data the equation could be used to find an optimal k to force the conversion to work for other solution concentrations.

The easiest way might be to multiply SG(15) by the density ratio of water at the two temperatures. But what fun is that? And I still need some data for comparison.

Any help?