  The proton temperature anisotropy in the solar wind exhibits apparent bounds
which are compatible with the theoretical constraints imposed by
temperature-anisotropy driven kinetic instabilities. Recent statistical
analyses based on conditional averaging indicate that near these theoretical
constraints the solar wind protons have typically enhanced temperatures and a
weaker collisionality. Here we carefully analyze the solar wind data and show
that these results are a consequence of superposition of multiple correlations
in the solar wind, namely, they mostly result from the correlation between the
proton temperature and the solar wind velocity and from the superimposed
anti-correlation between the proton temperature anisotropy and the proton
parallel beta in the fast solar wind. Colder and more collisional data are
distributed around temperature isotropy whereas hotter and less collisional
data have a wider range of the temperature anisotropy anti-correlated with the
proton parallel beta with signatures of constraints owing to the
temperature-anisotropy driven instabilities. However, most of the hot and
weakly collisional data, including the hottest and least collisional ones, lies
far from the marginal stability regions. Consequently, we conclude that there
is no clear relation between the enhanced temperatures and instability
constraints and that the conditional averaging used for these analyses must be
used carefully and need to be well tested.
