Plasma in post-CME current sheets (CSs) is expected to be highly turbulent because of the tearing and coalescence instability and/or local microscopic instabilities. For this reason, in the last decade the inconsistency between the observed ($10 4 Y10 5 km) and the expected ($1Y10 m) CS thickness has been tentatively explained in many MHD models as a consequence of plasma turbulence that should be able to significantly broaden the CS. However, from the observational point of view, little is known about this subject. A few post-CME CSs have been observed in UVCS spectra as a strong emission in the high-temperature [ Fe xviii] line, usually unobservable in the solar corona. In this work, published data on post-CME CSs observed by UVCS are reanalyzed, concentrating for the first time on the evolution of turbulence derived from the nonthermal broadening of the [Fe xviii] line profiles. Derived turbulent speeds are on the order of $60 km s À1 a few hours after the CME and slowly decay down to $30 km s À1 in the following 2 days. From this evolution the anomalous diffusivity due to microinstabilities has been estimated, and the scenario of multiple small-scale reconnections is tested. Results show that the existence of many ($10 À11 to 10 À17 CS m À3 ) microscopic CSs (CSs) of small sizes ($10Y10 4 m) could explain not only the high CS temperatures but also the much larger observed thickness of macroscopic CSs, thanks to turbulent broadening.