  In a recent work, Duong, Ghoul and Zaag determined the gradient profile for
blowup solutions of standard semilinear heat equation with power nonlinearities
in the (supposed to be) generic case. Their method refines the constructive
techniques introduced by Bricmont and Kupiainen and further developed by Merle
and Zaag. In this paper, we extend their refinement to the problem about the
reconnection of vortex lines with the boundary in a type-II superconductor
under planar approximation, a physical model derived by Chapman, Hunton and
Ockendon featuring the finite time quenching for the nonlinear heat equation
$$\frac{\partial h}{\partial t}=\frac{\partial^2 h}{\partial
x^2}+e^{-h}-\frac{1}{h^\beta},\quad\beta>0$$ subject to initial boundary value
conditions $$h(\cdot,0)=h_0>0,\quad h(\pm1,t)=1.$$ We derive the intermediate
extinction profile with refined asymptotics, and with extinction time $T$ and
extinction point $0$, the gradient profile behaves as $x\rightarrow0$ like
$$\lim_{t\rightarrow T}\,(\nabla
h)(x,t)\quad\sim\quad\frac{1}{\sqrt{2\beta}}\frac{x}{|x|}\frac{1}{\sqrt{|\log|x||}}\left[\frac{(\beta+1)^2}{8\beta}\frac{|x|^2}{|\log|x||}\right]^{\frac{1}{\beta+1}-\frac12},$$
agreeing with the gradient of the extinction profile previously derived by
Merle and Zaag. Our result holds with general boundary conditions and in higher
dimensions.
