  The functional RG (FRG) approach to pinning of $d$-dimensional manifolds is
reexamined at any temperature $T$. A simple relation between the coupling
function $R(u)$ and a physical observable is shown in any $d$. In $d=0$ its
beta function is displayed to a high order, ambiguities resolved; for random
field disorder (Sinai model) we obtain exactly the T=0 fixed point $R(u)$ as
well as its thermal boundary layer (TBL) form (i.e. for $u \sim T$) at $T>0$.
Connection between FRG in $d=0$ and decaying Burgers is discussed. An exact
solution to the functional RG hierarchy in the TBL is obtained for any $d$ and
related to droplet probabilities.
