The role of nuclear spin fluctuations in the dynamic polarization of nuclear spins by electrons is investigated in (In,Ga)As/GaAs quantum dots. The photoluminescence polarization under circularly polarized optical pumping in transverse magnetic fields (Hanle effect) is studied. A weak additional magnetic field parallel to the optical axis is used to control the efficiency of nuclear spin cooling and the sign of nuclear spin temperature. The shape of the Hanle curve is drastically modified when changing this control field, as observed earlier in bulk semiconductors and quantum wells. However, the standard nuclear spin cooling theory, operating with the mean nuclear magnetic field (Overhauser field), fails to describe the experimental Hanle curves in a certain range of control fields. This controversy is resolved by taking into account the nuclear spin fluctuations owed to the finite number of nuclei in the quantum dot. We propose a model considering cooling of the nuclear spin system by electron spins experiencing fast v