We study the role of magnetic monopoles at high enough temperature T>2Tc,
when they can be considered heavy, rare objects embedded into matter consisting
mostly of the usual "electric" quasiparticles, quarks and gluons. We review
available lattice results on monopoles at finite temperatures. Then we proceed
to classical and quantum charge-monopole scattering, solving the problem of
gluon-monopole scattering for the first time. We find that, while this process
hardly influences thermodynamic quantities, it does produce a large transport
cross section, significantly exceeding that for pQCD gluon-gluon scattering up
to quite high T. Thus, in spite of their relatively small density at high
T, monopoles are extremely important for QGP transport properties, keeping
viscosity small enough for hydrodynamics to work at LHC.Comment: 60 pages, 15 Figure