Simulation of the temperature distribution during the Pulse Electrochemical Machining (PECM) process provides information on system design and guidelines for practical use. The pulses that are applied to the PECM system have to be described on a time scale that can be orders of magnitude smaller than the time scale on which the thermal effects evolve. If the full detail of the applied pulses has to be taken into account, the time accurate calculation of the temperature distribution in PECM can become a computationally very expensive procedure. A new approach is introduced by time averaging the heat sources of the system. Performing this, the time steps used during the calculations are no longer dictated by the pulse characteristics. Using this approach, computationally very cheap, yet satisfactory results can be obtained. In this part of the work, the hybrid calculation and the Quasi Steady State ShortCut (QSSSC) are introduced. The hybrid calculation is a method, by which averaged and pulsed heat sources are combined in one calculation. The QSSSC is a method for quickly calculating the Quasi Steady State (QSS) in numerical calculations with time stepping. Analytical solutions of simplified cases are studied to provide useful insights into the more general case. It is shown that the averaging technique adopted in this work does not always deliver perfect results. However, using a technique of shifting the pulses in time, the results can become very satisfactory yet still extremely cheap. The more general case, which will be solved numerically, can be found in part II [Smets et al. J Appl Electrochem (Submitted)] of this work.