Out, Out And Away

When  $T=0$,  $g_T≠0$  so we have,  beyond the hot zone,

$g=g_T(T=0)e^{-\cfrac{x}{L}}$

where  $x=L$   is the extend of the hot zone.  If,

$g_T=\cfrac{G_{To}}{x}$  up to the hot zone,  then

$g_T(T=0)=\cfrac{G_{To}}{L}$

and

$g=\cfrac{G_{To}}{L}e^{-\cfrac{x}{L}}$

where  $x=0$  is on the boundary of  $T=0$.

Using the flux formulation, assuming no losses from  $x$  and beyond,

$g=\cfrac{G_{T}}{x^2}$

where  $G_T=L^2g_T(T=0)=LG_{To}$

$g=\cfrac{LG_{To}}{x^2}$

This gravity is positive outwards and drives all particles from within the hot zone into outer space.  Acting in the same region are, the gravity due to the mass of the hot body and gravity due to the mass of   $T$  (if this gravity exist).  Both of which are acting inwards.

Unfortunately,  $G_{To}=0$.