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.