Plastic injection molding is a versatile process, and a major part of the present plastic manufacturing industry. The traditional die design is limited to straight (drilled) cooling channels, which don't impart optimal thermal (or thermomechanical) performance. With the advent of additive manufacturing technology, injection molding tools with conformal cooling channels are now possible. However, optimum conformal channels based on thermomechanical performance are not found in the literature. This paper proposes a design methodology to generate optimized design configurations of such channels in plastic injection molds. The design of experiments (DOEs) technique is used to study the effect of the critical design parameters of conformal channels, as well as their cross-section geometries. In addition, designs for the "best" thermomechanical performance are identified. Finally, guidelines for selecting optimum design solutions given the plastic part thickness are provided.