Metastable austenitic stainless steel (MASS) has been the material of choice for the fabrication of disc springs employing incremental sheet forming (ISF) processes due to its high creep, fatigue, and chemical resistance, as well as its good surface quality. Previous research has shown that the presence of martensite enhances the formation of beneficial compressive residual stresses. However, if the ISF is accelerated to improve efficiency, the rise in temperature during ISF operation suppresses the deformation that causes martensite transition (DIMT). In essence, the cooling channel shapes are developed with numerical assistance such that its impact on residual stress induction is low. Variation in ISF process parameters, such as tool diameter, tool step-down, and contact force, as well as variation in cooling channel size, are used to construct the computational analysis. To analyze the finally produced residual stresses in the disc spring, the non-linear isotropic/kinematic hardening combined with the TRIP formulation is simulated. According to the comparison, the channel size must be between 0.8 and 1.2 mm in radius to minimize residual stress fluctuation. Additionally, when moving across the die with cooling channels, the force-controlled ISF produces more consistent results. Based on the numerical findings, it is conceivable to greatly enhance the ISF process speed and dissipate process heat by cooling the sheet on sides, allowing residual stresses and martensite content to be adjusted in a stable manner. As a result, the ISF process may be greatly expedited, making it more appealing for industrial applications.