  We examine the effects of cooling flows on the T_X-L_Bol relation for a
sample of the most X-ray luminous (L_Bol > 10^45 erg/s) clusters of galaxies
known. Using high-quality ASCA X-ray spectra and ROSAT images we explicitly
account for the effects of cooling flows on the X-ray properties of the
clusters and show that this reduces the previously-noted dispersion in the
T_X-L_Bol relationship. More importantly, the slope of the relationship is
flattened from L_Bol \propto T_{X}^3 to approximately L_Bol\propto T_{X}^2, in
agreement with recent theoretical models which include the effects of shocks
and preheating on the X-ray gas. We find no evidence for evolution in the
T_X-L_Bol relation within z~0.3. Our results demonstrate that the effects of
cooling flows must be accounted for before cosmological parameters can be
determined from X-ray observations of clusters. The results presented here
should provide a reliable basis for modelling the T_X-L_Bol relation at high
X-ray luminosities.
