  We investigate the grand potential of the one-dimensional Hubbard model in
the high temperature limit, calculating the coefficients of the high
temperature expansion ($\beta$-expansion) of this function up to order
$\beta^4$ by an alternative method. The results derived are analytical and do
not involve any perturbation expansion in the hopping constant, being valid for
arbitrary density of electrons in the one-dimensional model.
  In the half-filled case, we compare our analytical results for the specific
heat and the magnetic susceptibility, in the high-temperature limit, with the
ones obtained by Beni {\it et al.} and Takahashi's integral equations, showing
that the latter result does not take into account the complete energy spectrum
of the one-dimensional Hubbard model. The exact integral solution by J\"uttner
{\it et al}. is applied to the determination of the range of validity of our
expansion in $\beta$ in the half-filled case, for several different values of
$U$.
