We present the first results from a 2D VFP-PIC hybrid code for fast electron transport which solves the Vlasov–Fokker–Planck (VFP) equation for the background electrons using the code IMPACT. This new type of hybrid code captures full Braginskii electron transport including magnetization, non-local corrections and electron inertial effects. We consider propagation of a relativistic electron beam, generated by a laser of intensity I = (1–5) × 1019 W cm−2 and focal radius of a few microns, inside a near solid-density carbon target. Electron thermal transport out of the resistively heated background plasma is strong enough to compete with ohmic heating after about a picosecond. The effect of heat flow on the plasma temperature is sufficient to alter resistive magnetic field generation over time scales beyond a few picoseconds. This includes removal of beam-hollowing field near the beam injection point and re-emergence of a collimating magnetic field. Background electrons become weakly magnetized after a few picoseconds; enough for magnetized transport effects to significantly alter the evolution of the background plasma temperature and the long term evolution of the fast electron filaments. A practical estimate for the evolution of electron magnetization is presented and shown to agree with the simulation results. Non-local modifications to transport of up to 20% have been found in this situation.