The luminosity-temperature relation for clusters has a wide dispersion which has been explained as being due to a range of gas density or mass. We show here that the offset of a cluster from the mean relation is proportional to the strength of its cooling flow. We also confirm a similar effect on the metallicity-temperature relation. Since the cooling flow itself cannot produce such large effects, we propose that they are due to a more widespread difference between the intracluster media of cooling flow and non-cooling flow clusters. We suggest that the effects may be due to the inhomogeneity of the intracluster medium that is required in cooling flows to explain the distributed mass deposition. The effects have implications for the cluster temperature function and for the evolution of clusters.