Abstract Superconducting power supplies commonly known as flux pumps are becoming viable products in various industries. In this work we investigate magnetically switched ( J c ( B ) ) half-wave transformer rectifier flux pumps (TRFPs) via a simulation previously validated against an experimental system. Upgrades to the model are introduced, namely the transition to a fully hysteretic transformer reluctance model and the introduction of a conduction cooling thermal model. The conduction cooling model allows direct comparison between liquid cryogen and conduction cooled systems, highlighting the distinct variations in response. This study focuses on parameter sweeps over some of the most important aspects of a TRFP such as; input power, cooling paths and switch length. The findings from these variable sweeps shed light on how to best design the different aspects of a TRFP for most applications and the conclusions drawn throughout this work can be applied to most TRFP types. Some of the major findings from this work are; i. the need for dedicated cooling busses in TRFP switches, ii. that increased switch lengths increase voltage generation but negatively impact cooling effectiveness iii. that the reduction of the metallic coatings surrounding commercial coated conductors results in larger switch voltages.