  The goal of this work is to investigate the Faraday rotation measure (RM) of
radio galaxies in hot galaxy clusters in order to establish a possible
connection between the magnetic field strength and the gas temperature of the
intracluster medium. We performed Very Large Array observations at 3.6 cm and 6
cm of two radio galaxies located in A401 and Ophiuchus, a radio galaxy in
A2142, and a radio galaxy located in the background of A2065. All these galaxy
clusters are characterized by high temperatures. We obtained detailed RM images
at an angular resolution of 3'' for most of the observed radio galaxies. The RM
images are patchy and reveal fine substructures of a few kpc in size. Under the
assumption that the radio galaxies themselves have no effect on the measured
RMs, these structures indicate that the intracluster magnetic fields fluctuate
down to such small scales. These new data are compared with RM information
present in the literature for cooler galaxy clusters. For a fixed projected
distance from the cluster center, clusters with higher temperature show a
higher dispersion of the RM distributions (sigmaRM), mostly because of the
higher gas density in these clusters. Although the previously known relation
between the clusters X-ray surface brightness (Sx) at the radio galaxy location
and sigmaRM is confirmed, a possible connection between the sigmaRM-Sx relation
and the cluster temperature, if present, is very weak. Therefore, in view of
the current data, it is impossible to establish a strict link between the
magnetic field strength and the gas temperature of the intracluster medium.
