It is commonly recognized that one of the most effective ways to improve Brake-Specific Fuel Consumption (BSFC) in a spark-ignition engine at partial load is the adoption of VVA strategies, which largely affect the pumping work. Many different solutions have been proposed, characterized by different levels of complexity, effectiveness and costs. VVA systems currently available on the market allow for variable valve timing and/or lift (VVA). The design of a new mechanical VVA system has been discussed in Part I of this article. That study led to the development of a four-element VVA mechanism. Now, to estimate the potential advantages of the studied system on engine performances, one-dimensional thermo-fluid dynamic analyses were conducted, considering both full load and partial load operating conditions. For this reason, this article addresses the definition of the one-dimensional model of a 638-cm3 single-cylinder engine under development, which will be equipped with the four-element VVA system. The findings from the one-dimensional study will be discussed in detail. In particular, the parametric analyses, which concern the engine power at wide open throttle and the SFC at partial load, will be presented. These results, however, are only theoretical results because the one-dimensional simulation is not able to take into account the increased friction losses due to the complexity of the VVA system. Therefore, to correctly quantify the actual fuel consumption allowed by the studied system (net of the generally increased power dissipated by friction when compared to a conventional valve train), a specific methodology, discussed in Part I, has been adopted.