Effective thermal conductivities in the absence of mass diffusion have been measured near the lambda line of 3He-4He mixtures of up to 33% 3He concentration. The thermal conductivity in the normal phase has a rapidly increasing behavior as the temperature approaches the lambda point, but reaches a finite value there. Thermodiffusion ratios have also been measured, and show weak divergences--if any, weaker than logarithmic. Then, by using previous experimental values of the mass diffusivity given by Ahlers and Pobell, the thermal conductivity and the corresponding thermal diffusivity in the absence of the concentration gradient are deduced. The thermal diffusivity ....... 3 dtverges wtth a crtttcal exponent of approximately 1/3 wrespecttve of He concentration. The diffusivities Do and 192 corresponding respectively to the linewidths of the Rayleigh and the second-sound Brillouin scatterings in the superfluid phase are obtained: D2 diverges with a critical exponent of approximately 1/3 irrespective of 3He concentration, whereas Do does not diverge at all. As a whole, the mode-coupling theory on the basis of the dynamic scaling hypothesis has been proved to hold in the superfluid transition.