This paper investigated the influence of various twisted angles of fin inserts integrated on the inner heated pipe wall of a double-pipe heat exchanger by analysing the thermal–hydraulic performance through numerical simulations. Results showed twisted angle fin (TAF) induced turbulent fluid flow phenomena, generating transverse and longitudinal vortices, along with swirling flow. This collaboration between the vortices and swirling flow effectively prevents heat trapping and enhances heat transfer from the inner pipe wall through the intensive fluid mixing. Despite longitudinal swirling vortices and turbulence significantly enhance local and global heat transfer performance, they led to increased pressure drop. However, TAF twisting reduces pressure drop by streamlining flow. The performance evaluation criterion (PEC) value is a dimensionless quantity that facilitates the comprehensive evaluation of optimal configurations by comparing the increment in Nusselt number and the increment in friction factor. PEC values greater than 1 indicate that the increase in Nusselt number exceeded the increase in friction factor. Among tested configurations, the twisted fin angles of 60° (TAF60) exhibited the highest improvement in Nusselt number and friction factor, also achieving the highest PEC of 1.59712 at Reynolds number of 1194.71. TAF40 and TAF50 were identified as optimal configurations for enhancing the thermal–hydraulic efficiency, with average PEC values of 1.26893 and 1.27030, respectively. Overall, the study indicated a consistent enhancement trend with increasing twisted angles and emphasizes the significant thermal performance improvement of TAF configurations compared to the smooth conduit. Furthermore, the results showed a converging tendency across all TAF configurations in the percentage improvement in Nusselt number and friction factor, as well as PEC compared to the baseline No fin configuration with increasing Reynolds number, suggesting that future improvements in thermal–hydraulic performance are more dependent on geometric angles than fluid flow velocity.