  In this paper we study the influence of the magnetised thermal conductivity
on the propagation of a nanosecond $10^{14} \mathrm{Wcm}^{-2}$ laser in an
underdense plasma by performing simulations of a paraxial model laser in a
plasma with the full Braginskii magnetised transport coefficients. Analytic
theory and simulations show the shortening of the self-focal length of a laser
beam in a plasma as a result of the reduction of the plasma thermal
conductivity in a magnetic field. Furthermore the filamentation of a laser via
the thermal mechanism is found to have an increased spatial growth rate in a
magnetised plasma. We discuss the effect of these results on recent magnetised
inertial fusion experiments where filamentation can be detrimental to laser
propagation and uniform laser heating. We conclude the application of external
magnetic fields to laser-plasma experiments requires the inclusion of the
extended electron transport terms in simulations of laser propagation.
