Deep cooling of electron and nuclear spins is equivalent to achieving polarization degrees close to 100% and is a key requirement in solid-state quantum information technologies(1-7). While polarization of individual nuclear spins in diamond(2) and SiC (ref. 3) reaches 99% and beyond, it has been limited to 50-65% for the nuclei in quantum dots(8-10). Theoretical models have attributed this limit to formation of coherent 'dark' nuclear spin states(11-13) but experimental verification is lacking, especially due to the poor accuracy of polarization degree measurements. Here we measure the nuclear polarization in GaAs/AlGaAs quantum dots with high accuracy using a new approach enabled by manipulation of the nuclear spin states with radiofrequency pulses. Polarizations up to 80% are observed-the highest reported so far for optical cooling in quantum dots. This value is still not limited by nuclear coherence effects. Instead we find that optically cooled nuclei are well described within a classical spin temperature framework(14). Our findings unlock a route for further progress towards quantum dot electron spin qubits where deep cooling of the mesoscopic nuclear spin ensemble is used to achieve long qubit coherence(4,5). Moreover, GaAs hyperfine material constants are measured here experimentally for the first time.