  We calculate the low temperature spectral function of one-dimensional
incommensurate charge density wave (CDW) states and half-filled Mott insulators
(MI). At $T=0$ there are two dispersing features associated with the spin and
charge degrees of freedom respectively. We show that already at very low
temperatures (compared to the gap) one of these features gets severely damped.
We comment on implications of this result for photoemission experiments.
