Upflows of several tens of km/s have been observed by SOHO-CDS in the late gradual phase of the M6.8 two-ribbon flare on April 29, 1998. These upflows observed in EUV lines formed at coronal temperatures are interpreted as chromospheric evaporation which fills the post-flare loops with hot plasma. In order to achieve chromospheric evaporation, the chromospheric plasma has to be heated to coronal temperatures. The energy for this heating process is assumed to be provided by magnetic reconnection. The mechanism which transports the energy from the reconnection site to the chromosphere must be either thermal or non-thermal. We compare the observed upflow velocities with the velocities derived by different chromospheric heating models in order to decide which mechanism might account for the chromospheric heating. From non-thermal models we take the electron energy flux necessary to achieve the observed velocities and calculate the expected hard X-ray counts in Yohkoh/HXT for non-thermal thick-target Bremsstrahlung generated by this electron flux. We conclude that energetic (> 15keV) non-thermal electrons are unlikely to cause the chromospheric heating since a significant number of HXT counts are expected from the resulting electron energy flux but not observed. Recent thermal conduction models seem to be more appropriate for explaining the observations.