To investigate core plasma heating in fast ignition, a relativistic Fokker-Planck code for fast electrons is developed in a one-dimensional planar coordinates system. It is found that in dense plasmas, the Joule heating is much smaller than the heating through Coulomb interactions. In the latter energy deposition process, the long-range collective effect is comparable to that of binary electron-electron collisions. Moreover, on the basis of coupled transport-hydrodynamic simulations in one-dimensional planar geometry, the core heating process for an ignition-experiment-grade compressed core (R = 0.3 g/cm2) is examined, and a possibility of evaluation of burn history from the neutron spectrum is shown. It is shown that a relatively low energy component (E0 1 MeV) of electron beams plays an important role for effective core heating in fast ignition.