  We study clusters in the BCS cluster sample which are observed by Chandra and
are more distant than redshift, z>0.1. We select from this subsample the
clusters which have both a short central cooling time and a central temperature
drop, and also those with a central radio source. Six of the clusters have
clear bubbles near the centre. We calculate the heating by these bubbles and
express it as the ratio r_heat/r_cool=1.34+/-0.20. This result is used to
calculate the average size of bubbles expected in all clusters with central
radio sources. In three cases the predicted bubble sizes approximately match
the observed radio lobe dimensions.
  We combine this cluster sample with the B55 sample studied in earlier work to
increase the total sample size and redshift range. This extended sample
contains 71 clusters in the redshift range 0<z<0.4. The average distance out to
which the bubbles offset the X-ray cooling in the combined sample is at least
r_heat/r_cool=0.92+/-0.11. The distribution of central cooling times for the
combined sample shows no clusters with clear bubbles and t_cool>1.2Gyr. An
investigation of the evolution of cluster parameters within the redshift range
of the combined samples does not show any clear variation with redshift.
