  We derive analytical expressions for the spectral moments of the dynamical
response functions of the Hubbard model using the high-temperature series
expansion. We consider generic dimension $d$ as well as the infinite-$d$ limit,
arbitrary electron density $n$, and both finite and infinite repulsion $U$. We
use moment-reconstruction methods to obtain the one-electron spectral function,
the self-energy, and the optical conductivity. They are all smooth functions at
high-temperature and, at large-$U$, they are featureless with characteristic
widths of order the lattice hopping parameter $t$. In the infinite-$d$ limit we
compare the series expansion results with accurate numerical renormalization
group and interaction expansion quantum Monte-Carlo results. We find excellent
agreement down to surprisingly low temperatures, throughout most of the
bad-metal regime which applies for $T \gtrsim (1-n)D$, the Brinkman-Rice scale.
The resistivity increases linearly in $T$ at high-temperature without
saturation. This results from the $1/T$ behaviour of the compressibility or
kinetic energy, which play the role of the effective carrier number. In
contrast, the scattering time (or diffusion constant) saturate at high-$T$. We
find that $\sigma(n,T) \approx (1-n)\sigma(n=0,T)$ to a very good approximation
for all $n$, with $\sigma(n=0,T)\propto t/T$ at high temperatures. The
saturation at small $n$ occurs due to a compensation between the
density-dependence of the effective number of carriers and that of the
scattering time. The $T$-dependence of the resistivity displays a knee-like
feature which signals a cross-over to the intermediate-temperature regime where
the diffusion constant (or scattering time) start increasing with decreasing
$T$. At high-temperatures, the thermopower obeys the Heikes formula, while the
Wiedemann-Franz law is violated with the Lorenz number vanishing as $1/T^2$.
