We analyze the importance of self-heating effects in a new cold cathode emitter which consists of a thin region of cadmium sulfide (CdS) sandwiched between a heavily doped indium phosphide (InP) substrate and a low work function lanthanum sulfide (LaS) semimetallic thin film. We identify the mechanisms leading to power dissipation in a cathode with an emission window of rectangular geometry, including the effects of inelastic scattering in the CdS and LaS layers. The latter are modeled using a temperature dependent mean-free path approach. The analysis includes the effects of current crowding in the emission window due to the finite resistivity of the LaS layer. We determine the cathode parameters which minimize current crowding and self-heating effects in the cathode. We also calculate the relative contribution of the ballistic and inelastic portions of the electron current emitted into vacuum.