The indirectly heated cathode (IHC) Bernas source is used in plasma process devices as it can produce a high current of desired ion species. The formation of various ion species is associated with the complex electron production mechanism inside the source, including beam plasma interaction and energy relaxation. However, plasma diagnostics inside IHC sources has been limited by the assumption of a Maxwellian distribution. In this work, the discharge characteristics of IHC plasmas were investigated by analyzing the electron energy probability functions (EEPFs) under various conditions. The shape of the EEPF is dominantly affected by the voltage applied to the hot-cathode and repeller (i.e., cathode voltage), whereby the kinetic energy of the beam electrons is determined. With increasing cathode voltage, the EEPFs show a bi-Maxwellian-like distribution with the bulk and energetic electron groups. The thermalization among the two electron groups with increasing magnetic field makes the EEPFs to follow a Maxwellian distribution. The absolute value of the density and effective temperature of the electron are mainly governed by the bulk electron group with a relatively higher density, and the changes in the electric potentials are explained in the context of the confinement of the energetic electrons.