Both observation and theory reveal a close relationship between the kinematics of coronal mass ejections (CMEs) and the thermal energy release traced by the related soft X-ray (SXR) emission. The major problem of empirical studies of this relationship is the distortion of the CME speed by the projection effect in the coronagraphic measurements. We present a re-assessment of the statistical relationship between CME velocities and SXR parameters, using the SOHO/LASCO catalog and GOES whole Sun observations during the period 1996 to 2008. 49 events were identified where CMEs originated near the limb, at central meridian distances between 70• and 85• , and had a reliably identified SXR burst, the parameters of which -peak flux and fluence -could be determined with some confidence. We find similar correlations between the logarithms of CME speed and of SXR peak flux and fluence as several earlier studies, with correlation coefficients of 0.48 and 0.58, respectively. Correlations are slightly improved over an unrestricted CME sample when only limb events are used. However, a broad scatter persists. We derive the parameters of the CME-SXR relationship and use them to predict ICME arrival times at Earth. We show that the CME speed inferred from SXR fluence measurements tends to perform better than SoHO/LASCO measurements in the prediction of ICME arrival times near 1 AU. The estimation of the CME speed from SXR observations can therefore make a valuable contribution to space weather predictions.