Rotationally inelastic collisions of O2 with He in the 10-34 K thermal range are investigated by means of an experimental procedure based on supersonic gas jets probed by Raman spectroscopy. The procedure employs a kinetic master equation (MEQ) that describes the time evolution of the rotational populations of O2 along supersonic jets of O2 and He mixtures. The MEQ is expressed in terms of experimental quantities (number density and rotational populations) measured here, and state-to-state rate coefficients for the O2:He inelastic collisions calculated here, plus those for O2:O2 collisions from the literature. An agreement with the experiments is accomplished for temperatures between 10 and 34 K. Within this thermal range, the role of the fine structure due to electron spin in the collision dynamics of O2 is discussed.