The bulk helimagnet Cu2OSeO3 represents a unique example in the family of B20 cubic helimagnets exhibiting a tilted spiral and skyrmion phase at low temperatures when the magnetic field is applied along the easy (001) crystallographic direction. Here we present a systematic study of the stability and ordering of these low-temperature magnetic states. We focus our attention on the temperature and field dependencies of the tilted spiral state that we observe persisting up to above T=35 K, i.e., up to higher temperatures than reported so far. We discuss these results in the frame of the phenomenological theory introduced by Dzyaloshinskii in an attempt to reach a quantitative description of the experimental findings. We find that the anisotropy constants, which are the drivers behind the observed behavior, exhibit a pronounced temperature dependence. This explains the differences in the behavior observed at high temperatures (above T=18 K), where the cubic anisotropy is weak, and at low temperatures (below T=18 K), where a strong cubic anisotropy induces an abrupt appearance of the tilted spirals out of the conical state and enhances the stability of skyrmions. @en