  We present time-dependent density matrix renormalization group (DMRG) results
for strongly interacting one dimensional fermionic systems at finite
temperature. When interactions are strong the characteristic spin energy can be
greatly suppressed relative to the characteristic charge energy, allowing for
the possibility of spin-incoherent Luttinger liquid physics when the
temperature is high compared to the spin energy, but small compared to the
charge energy. Using DMRG we compute the spectral properties of the $t-J$ model
at arbitrary temperatures with respect to both spin and charge energies. We
study the full crossover from the Luttinger liquid regime to the
spin-incoherent regime,focusing on small $J/t$, where the signatures of
spin-incoherent behavior are more manifest. Our method allows us to access the
analytically intractable regime where temperature is of the order of the spin
energy, $T\sim J$. Our results should be helpful in the interpretation of
experiments that may be in the crossover regime, $T\sim J$, and apply to
one-dimensional cold atomic gases where finite-temperature effects are
appreciable. The technique may also be used to guide the development of
analytical approximations for the crossover regime.
