  The effective string picture of confinement is used to derive theoretical
predictions for the interquark potential at finite temperature. At short
distances, the leading string correction to the linear confining potential
between a heavy quark-antiquark pair is the "L\"uscher term''. We assume a
Nambu--Goto effective string action, and work out subleading contributions in
an analytical way. We discuss the contribution given by a possible ``boundary
term'' in the effective action, comparing these predictions with results from
simulations of lattice $Z_2$ gauge theory in three dimensions, obtained with an
algorithm which exploits the duality of the $Z_2$ gauge model with the Ising
spin model.
