The role of self generated magnetic fields in the transport of a heat wave following a nanosecond laser irradiation of a solid target is investigated. Magnetic fields are expected to localize the electron carrying the heat flux but at the same time are affected in their evolution by the heat flux itself. We performed simultaneous measurements of heat wave propagation velocity within the target and magnetic fields developing on the target surface. These were compared to results obtained by numerical magneto-hydrodynamic modeling, including self-generated B fields. The comparison shows that longitudinal heat flow is overestimated in the simulations. Similarly, but most notably, the radial expansion of the magnetic fields is underestimated by the modeling. The two are likely linked, the more pronounced radial drift of B-fields induces a rotation of heat flux in the radial direction, and corresponding longitudinal heat flux inhibition. This suggests the need for improving present modeling of self-generated magnetic fields evolution in high power laser-matter interaction.