The energy released by a relativistic electron beam at the interaction with material samples produces a thermal field that can affect their physical integrity. Such situations are found in fusion technology where streams of energetic electrons can destroy the walls of the machine. In this paper we present an experimental and a theoretical semi-analytical study of these thermal fields induced in graphite with a density of 2.23 g/cm3 by a 6.23 MeV electron beam obtained from a LINAC. The average power of the electron beam is 62 W. A sample with a reduced size is considered (1 cm × 1 cm × 1.5 cm) having a surface comparable with the beam cross section. The main conclusion of our study is that for small samples the heat source term (especially during heating process) and the boundary conditions (especially during cooling process) are key elements in determining the thermal field in the sample volume. Extrapolations are made for larger samples (up to 1 m) and higher electron beam currents (up to 0.7 MA).