= Solution
In the <radiative-zero white-dwarf envelope>, $dP/dT=(17/4)P/T=(17/4)\mathcal R\rho$. Substitute this derivative into the <stellar hydrostatic equation>:
$$
\frac{17}{4}\mathcal R\rho\frac{dT}{dr}=-\frac{GM\rho}{r^2},\qquad
\frac{dT}{dr}=-\frac4{17}\frac{GM}{\mathcal Rr^2}.
$$
Integrating from the idealized zero-temperature surface at $R$ gives
$$
\boxed{T(r)=\frac4{17}\frac{GM}{\mathcal R}\left(\frac1r-\frac1R\right)
=\frac4{17}\frac{\mu m_H}{k}GM\left(\frac1r-\frac1R\right).}
$$
This also gives $d\log T/d\log P=4/17$. A finite surface <temperature> adds $T_s$ to the integrated profile if the pure power-law <pressure> relation is retained locally. Near the actual <photosphere>, the integration constant in the <pressure> law also matters; the displayed expression is the radiative-zero limit implicit in the printed result and accurate in the deep envelope when $T_c\gg T_{\rm eff}$.
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