High-resolution thermal-conductivity measurements near the lambda point of helium

Measurements of the thermal conductivity of helium in the region from 6 x 10 to the -8th to 6 x 10 to the -4th K above the lambda point at the vapor pressure are reported. Within 5 x 10 to the -6th K of the transition conductivity values are found significantly lower than expected on the basis of theoretical extrapolations from previous experiments. When the parameter Rk is calculated, a maximum about 2 x 10 to the -6th K above the transition is found, in disagreement with the predictions of the two-loop dynamic renormalization-group theory. The uncertainties in the results in this region are discussed in detail.