  The cubic $\beta$-Mn-type alloy Co$_8$Zn$_8$Mn$_4$ is a chiral helimagnet
that exhibits a peculiar temperature-dependent behavior in the spiral pitch,
which decreases from 130 nm at room temperature to 70 nm below 20 K. Notably,
this shortening is also accompanied by a structural transition of the
metastable skyrmion texture, transforming from a hexagonal lattice to a square
lattice of elongated skyrmions. The underlying mechanism of these
transformations remain unknown, with interactions potentially involved
including temperature-dependent Dzyaloshinskii-Moriya interaction,
magnetocrystalline anisotropy, and exchange anisotropy. Here, x-ray resonant
magnetic small-angle scattering in vectorial magnetic fields was employed to
investigate the temperature dependence of the anisotropic properties of the
helical phase in Co$_8$Zn$_8$Mn$_4$. Our results reveal quantitatively that the
magnitude of the anisotropic exchange interaction increases by a factor of 4 on
cooling from room temperature to 20 K, leading to a 5% variation in the helical
pitch within the (001) plane at 20 K. While anisotropic exchange interaction
contributes to the shortening of the spiral pitch, its magnitude is
insufficient to explain the variation in the spiral periodicity from room to
low temperatures. Finally, we demonstrate that magnetocrystalline and exchange
anisotropies compete, favoring different orientations of the helical vector in
the ground state.
