The physics of interacting nuclear spins in solids is well interpreted within the nuclear spin temperature concept. A common approach to cooling the nuclear spin system is adiabatic demagnetization of the initial, optically created, nuclear spin polarization. Here, the selective cooling of ⁷⁵As spins by optical pumping followed by adiabatic demagnetization in the rotating frame is realized in a nominally undoped GaAs/(Al,Ga)As quantum well. The lowest nuclear spin temperature achieved is 0.54 μK. The rotation of 6 kG strong Overhauser field at the ⁷⁵As Larmor frequency of 5.5 MHz is evidenced by the dynamic Hanle effect. Despite the presence of the quadrupole induced nuclear spin splitting, it is shown that the rotating ⁷⁵As magnetization is uniquely determined by the spin temperature of coupled spin-spin and quadrupole reservoirs. The dependence of heat capacity of these reservoirs on the external magnetic field direction with respect to crystal and structure axes is investigated.