In this paper we analyze the temperature anisotropy of velocity distribution functions (VDFs) of protons measured by the Helios spacecraft in fast solar wind. We concentrate on data obtained during the primary mission, including the first perihelion passage, of Helios 2 in a distance range between 0.98 and 0.29 AU for the days 23 through 114 of the year 1976. The main goal is to provide solid statistical evidence on the relation between the anisotropy and the proton plasma beta, parameters that play a key role in the regulation of the shape of the core. It is believed to be formed by resonant interactions between ion cyclotron waves and protons, as described by the quasi-linear theory of pitch angle diffusion. In the analysis of the VDF, particular attention is paid to the symmetry axis, which can be determined by the directions of either the magnetic field, the proton heat flux, or the alpha-proton relative drift. We analyze in detail the core part of the proton VDF, carefully avoiding a possible influence of the proton beam component.