Just from my own experience, I would have to say that for severe engorgement
cold can actually work better because it reduces the swelling caused by edema
thereby letting the milk flow more easily.  For mastitis, however, I would
personally recommend heat as heat relaxes the milk ducts and allows the milk
to flow more freely.  Or for trying to pump, or increse the milk supply, heat
and massage I would think would work the best.
For initial engorgement...cold after and between feelings to reduce swelling,
heat right before nursing to relax milk ducts????

Kim Sherwood, LLLL, in upstate NY