Slow cooling relieves internal stresses of metals. Plastics, especially ones with more crystaline (less amorphous) structure shrinks more as they cool slowly. Slower cooling promotes more internal crystaline structure, which is more brittle and shrinks more. If you want a more dimensional stable part, when the injection mold opens, drop the part into cold water (it will have less internal stress. Think of the melted plastic having no internal stresses. Then as it cools in the mold with varying rates, stresses are formed. Plastic parts shrink more when then they cool slowly.
Slower cooling does usually relieve some of the molded in stress. Many products are annealed after injection molding just for this purpose. The other factor that affects the linier stress is the velocity. At slower velocities a greater amount of stress in the direction of flow occurs. Of course faster velocities used to achieve a consistent viscosity will tend to entrap more air. Venting is very important. There must be vents along the entire flow path, not just at the end of fill. Weak weld lines may also become more evident after annealing, shrinkage will increase.
We had a part that as soon as the injection mold opened, the operator clamped it into a water cooled aluminum fixture. This cooled the part IN THE SHAPE IT NEEDED TO BE FOR INSTALLTION.
Ultra-Violet (sun) light and certain chemicals may cause cracking. The black dye may serve as UV Stabilizer and LDPE is not prone to chemical attack or moisture absorption.
I worked with molded plastic bodywork on motorcycles with complex contoured shapes. Those parts tend to crack where the fastener holes are when gasoline is spilled on them. (Where there is a knit line from the plastic flowing around the core pin and knitting back together). A rubber washer and limiting the fastener torque helped reduce cracking.