We study a steady state, bearing a heat current, Q(0). In the normal s
tate of liquid He-4 with constraining geometry, near the lambda point,
at temperatures T greater than the lambda temperature, T-lambda. Crit
ical order parameter fluctuations near the boundary are incorporated i
n the expression for the non-local thermal resistivity. The Kapitza re
sistance is manifested by the additional temperature rise at the bound
ary, as compared with the bulk-extrapolated value. Sensitivity of the
calculations to the application of the Dirichlet boundary condition is
discussed. (C) 1998 American Institute of Physics.