ABSTRACT The large temperature difference between cold gas clouds around galaxies and the hot haloes that they are moving through suggests that thermal conduction could play an important role in the circumgalactic medium. However, thermal conduction in the presence of a magnetic field is highly anisotropic, being strongly suppressed in the direction perpendicular to the magnetic field lines. This is commonly modelled by using a simple prescription that assumes that thermal conduction is isotropic at a certain efficiency f < 1, but its precise value is largely unconstrained. We investigate the efficiency of thermal conduction by comparing the evolution of 3D hydrodynamical (HD) simulations of cold clouds moving through a hot medium, using artificially suppressed isotropic thermal conduction (with f), against 3D magnetohydrodynamical (MHD) simulations with (true) anisotropic thermal conduction. Our main diagnostic is the time evolution of the amount of cold gas in conditions representative of the lower (close to the disc) circumgalactic medium of a Milky-Way-like galaxy. We find that in almost every HD and MHD run, the amount of cold gas increases with time, indicating that hot gas condensation is an important phenomenon that can contribute to gas accretion on to galaxies. For the most realistic orientations of the magnetic field with respect to the cloud motion we find that f is in the range 0.03–0.15. Thermal conduction is thus always highly suppressed, but its effect on the cloud evolution is generally not negligible.