  In a classical ideal plasma, a magnetic field is known to reduce the heat
conductivity perpendicular to the field whereas it does not alter the one along
the field. Here we show that, in strongly correlated plasmas that are observed
at high pressure or/and low temperature, a magnetic field reduces the
perpendicular heat transport much less and even {\it enhances} the parallel
transport. These surprising observations are explained by the competition of
kinetic, potential and collisional contributions to the heat conductivity. Our
results are based on first principle molecular dynamics simulations of a
one-component plasma.
