Despite the increasing interest in supercritical carbon dioxide (sCO2) cycles in place of Rankine cycles for power generation, there is limited information available on the design and off-design performance of mechanical air-cooled heat rejection systems for sCO2 power cycles. In this work, the conceptual design and thermofluid system modelling of an air-cooled heat exchanger (ACHE) system for a 50 MWe sCO2 CSP plant is presented. The design includes the selection of major components for the ACHE system including the piping, fan, and finned-tube bundle, as well as the development of an in-house thermofluid model of the system using Python. A model of the system was also developed using the commercial code Flownex to simulate off-design conditions. To limit auxiliary power consumption, sCO2 ACHEs require deep finned-tube bundles with forced-draft fans that operate at a relatively high static pressure rise, and a relatively low volume flow rate. The results show that flow bypass combined with fan on-off control is an effective method to maintain a bulk outlet sCO2 temperature. However, to prevent local over-cooling to temperatures below the critical point, fan speed control is required. Additionally, employing fan speed control significantly lowers auxiliary power consumption relative to bypass control.