  We study the dynamical response of the half-filled one-dimensional(1d)
Hubbard model for a range of interaction strengths $U$ and temperatures $T$ by
a combination of numerical and analytical techniques. Using time-dependent
density matrix renormalization group (tDMRG) computations we find that the
single-particle spectral function undergoes a crossover to a spin-incoherent
Luttinger liquid regime at temperatures $T \sim J=4t^2/U$ for sufficiently
large $U > 4t$. At smaller values of $U$ and elevated temperatures the spectral
function is found to exhibit two thermally broadened bands of excitations,
reminiscent of what is found in the Hubbard-I approximation. The dynamical
density-density response function is shown to exhibit a finite temperature
resonance at low frequencies inside the Mott gap, with a physical origin
similar to the Villain mode in gapped quantum spin chains. We complement our
numerical computations by developing an analytic strong-coupling approach to
the low-temperature dynamics in the spin-incoherent regime.
