As for the cooling effects on balance, there have been studies done where the inside cavities are cooled and no cooling on the outside cavities to try and reduce imbalance since it was once thought that a thermal imbalance existed in the molds and that created the imbalance. It sounded good and we have all used that explanation before. But the results of the test mentioned showed little to no change in imbalance when varying individual inside and outside cavity/core temps 100F or more.
This is supported by a few points in the study. For one, you will see imbalances on the first shots and not only once the tool heats up and it thermally stable, or if you short shoot with no cooling - simply put the mold in and do a short shot. Also cooling has little impact on short shot filling. Cooling has more of an impact on cosmetics, packing, etc...as the above tests indicate.
Take care and have fun,
Dave