Time-dependent computational simulations using both single-fluid O-D and two-fluid 1 1/2-D models are developed for and utilized in an investigation of the ohmic heating of a Spheromak plasma. The plasma density and composition, the applied magnetic field strength, the plasma size, and the plasma current density profile are considered for their effects on the Spheromak heating rate and maximum achievable temperature. The feasibility of ohmic ignition of a reactor-size pheromak plasma is also contemplated.