  The heat equation is considered in the complex medium consisting of many
small bodies (particles) embedded in a given material. On the surfaces of the
small bodies an impedance boundary condition is imposed. An equation for the
limiting field is derived when the characteristic size $a$ of the small bodies
tends to zero, their total number $\mathcal{N}(a)$ tends to infinity at a
suitable rate, and the distance $d = d(a)$ between neighboring small bodies
tends to zero: $a << d$, $\lim_{a\to 0}\frac{a}{d(a)}=0$. No periodicity is
assumed about the distribution of the small bodies. These results are basic for
a method of creating a medium in which heat signals are transmitted along a
given line. The technical part for this method is based on an inverse problem
of finding potential with prescribed eigenvalues.
