The efficiency of optical cooling of nuclear spins in a CdTe/CdZnTe quantum well is investigated as a function of an external magnetic field. Our results confirm that there is indeed an optimal external magnetic field for optical cooling. We associate it with the kinetic local field $B_{KL}$ defined by the heating rate of the spin-spin reservoir due to the fluctuations of the hyperfine interaction. We also propose an experimental technique for measuring $B_{KL}$. For our sample we find that $B_{KL}=1.0\pm0.4$ G and it is independent of the electron polarization and pump power. The measured values of the kinetic local fields are in good agreement with a theoretical calculation $B_{KL} = 0.7$ G, taking into account indirect spin-spin interactions of Cd and Te nuclear spins and their considerably different hyperfine constants. The hyperfine constants of the magnetic isotopes of Cd and Te in CdTe are estimated.