We present a Chandra study of 38 X-ray luminous clusters of galaxies in the ROSAT Brightest Cluster Sample ( BCS ) that lie at moderate redshifts ( z \approx 0.15 –0.4 ) . Based primarily on power ratios and temperature maps , we find that the majority of clusters at moderate redshift generally have smooth , relaxed morphologies with some evidence for mild substructure perhaps indicative of recent minor merger activity . Using spatially-resolved spectral analyses , we find that cool cores appear to still be common at moderate redshift . At a radius of 50 kpc , we find that at least 55 per cent of the clusters in our sample exhibit signs of mild cooling ( t _ { cool } < 10 Gyr ) , while in the central bin at least 34 per cent demonstrate signs of strong cooling ( t _ { cool } < 2 Gyr ) . These percentages are nearly identical to those found for luminous , low-redshift clusters of galaxies , indicating that there appears to be little evolution in cluster cores since z \approx 0.4 and suggests that heating and cooling mechanisms may already have stabilised by this epoch . Comparing the central cooling times to catalogues of central H \alpha emission in BCS clusters , we find a strong correspondence between the detection of H \alpha and central cooling time . We also confirm a strong correlation between the central cooling time and cluster power ratios , indicating that crude morphological measures can be used as a proxy for more rigorous analysis in the face of limited signal-to-noise data . Finally , we find that the central temperatures for our sample typically drop by no more than a factor of \sim 3–4 from the peak cluster temperatures , similar to those of many nearby clusters .