The temperature dependence of the effective kinematic viscosity of turbulent He II, nu(eff)(T) , is deduced from second sound attenuation data using the late stage of decay of thermally induced counterflow He II turbulence in two channels of square cross section. It is shown to qualitatively agree with the published data for nu(eff)(T) calculated based on experiments on decaying-grid-generated He II turbulence [Niemela, J. Low Temp. Phys. 138, 537 (2005)]. Corrections to these data due to the "sine squared" law that describes attenuation of the second sound wave propagating along an arbitrary direction with respect to the direction of the core of a quantized vortex in turbulent He II are discussed and applied.