Rotationally inelastic collisions of O-2 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 O-2 along supersonic jets of O-2 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 O-2 :He inelastic collisions calculated here, plus those for O-2 : O-2 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 O-2 is discussed.