  We consider the proximity effect between Dirac states at the surface of a
topological insulator and a ferromagnet with easy plane anisotropy, which is
described by the \emph{XY}-model and undergoes a
Berezinskii-Kosterlitz-Thouless (BKT) phase transition. The surface states of
the topological insulator interacting with classical magnetic fluctuations of
the ferromagnet can be mapped onto the problem of Dirac fermions in a random
magnetic field. However, this analogy is only partial in the presence of
electron-hole asymmetry or warping of the Dirac dispersion, which results in
screening of magnetic fluctuations. Scattering at magnetic fluctuations
influences the behavior of the surface resistivity as a function of
temperature. Near the BKT phase transition temperature we find that the
resistivity of surface states scales linearly with temperature and has a clear
maximum which becomes more pronounced as the Fermi energy decreases.
Additionally at low temperatures we find linear resistivity, usually associated
with non-Fermi liquid behavior, however here it appears entirely within the
Fermi liquid picture.
