Recent in-situ determinations of the temporal evolution of the charge state distribution in the fast and slow solar wind have shown a general decrease in the degree of ionization of all the elements in the solar wind along solar cycles 23 and 24. Such a decrease has been interpreted as a cooling of the solar corona which occurred during the decline and minimum phase of solar cycle 23 from 2000 to 2010. In the present work, we investigate whether spectroscopic determinations of the temperature of the quiescent streamers show signatures of coronal plasma cooling during cycles 23 and 24. We measure the coronal electron density and thermal structure at the base of 60 quiescent streamers observed from 1996 to 2013 by SOHO/SUMER and Hinode/EIS and find that both quantities do now show any significant dependence on the solar cycle. We argue that if the slow solar wind is accelerated from the solar photosphere or chromosphere, the measured decrease in the in-situ wind charge state distribution might be due to an increased efficiency in the wind acceleration mechanism at low altitudes. If the slow wind originates from the corona, a combination of density and wind acceleration changes may be responsible for the in-situ results.