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(-1)) 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 proportional to T-X(3) to approximately L-Bol proportional to T-X(2), in agreement with recent theoretical models which include the effects of shocks and pre-heating on the X-ray gas. We find no evidence for evolution in the T-X-L-Bol relation within z similar to 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.