The energy dissipation of quasiclassical homogeneous turbulence in superfluid (He II) is controlled by an effective kinematic viscosity , which relates the energy decay rate to the density of quantized vortex lines as . The precise value of is of fundamental importance in developing our understanding of the dissipation mechanism in He II, and it is also needed in many high-Reynolds-number turbulence experiments and model testing that use He II as the working fluid. However, a reliable determination of requires the measurements of both and , which was never achieved. Here we discuss our study of the quasiclassical turbulence that emerges in the decay of thermal counterflow in He II above 1 K. We were able to measure by using a recently developed flow-visualization technique and via second-sound attenuation. We report the values in a wide temperature range determined from a comparison of the time evolution of and .