Finite-size effects on the thermal conductivity of ^4He near T_\lambda

We present results of a renormalization-group calculation of the thermal conductivity of confined $\rm^4$He in a $L^2 \times \infty$ geometry above and at $T_\lambda$ within model F with Dirichlet boundary conditions for the order parameter. We assume a heat flow parallel to the boundaries which implies Neumann boundary conditions for the entropy density. No adjustable parameters other than those known from bulk theory and static finite-size theory are used. Our theoretical results are compared with experimental data by Kahn and Ahlers.