Correct modeling of the electron-energy transport is essential for inertial confinement fusion target design. Various transport models have been proposed in order to extend the validity of a hydrodynamical description into weakly collisional regimes, taking into account the nonlocality of the electron transport combined with the effects of self-generated magnetic fields. We have carried out new experiments designed to be highly sensitive to the modeling of the heat flow on the Ligne d'Intégration Laser facility, the prototype of the Laser Megajoule. We show that two-dimensional hydrodynamic simulations correctly reproduce the experimental results only if they include both the nonlocal transport and magnetic fields.