Mold cooling is one of the most important phases in the molding cycle, comprising more than half of the total cycle time. This affects the final quality of the part and the production rate of the mold. Therefore, the design of a mold cooling channel system is essential to improve its thermal management and achieve a better control over the cycle time. The hardening of small thin wall plastic parts with complex geometries is one of the most challenging problems in the plastics injection industry, since we need to ensure quality, distortionfree plastic parts. The solution lies in optimizing the cooling system, particularly the case of mold inserts with unconventional geometries compatible with the geometry of the part. Using the constructal principle, we develop a channel configuration as an umbrella for cooling a mold insert volume. This configuration includes a central channel transporting the coolant until the tip of the mold insert where a certain number of divergent channels depart performing the fluid flow return. A relation for the svelteness allows determining the channels sizes to ensure negligible local head losses, depending on the angle and number of divergent channels. Svelteness orientates the evolution of the flow towards smaller secondary channels returning the flow with higher divergent angles.