I'll admit I'm listening with an open mind to this discussion. I realize
that the arguments are not always backed up by solid research, mostly
anecdotal experience. But I've always had good results with BRIEF
amounts of heat followed by pumping (even beofre latching on if the
nipple is flattened) and letting the baby do the rest. Feeding can be
followed by cool (not ice) compresses. Moms always say "that feels so
good" when we use the heat first.  And my argument is that the breast is
a gland, not a muscle like a sprained ankle, and we want that gland to
produce.  The patient population I work with is very adamant against
cold and ice use after childbirth. They keep the baby and the breasts
warm!
In the UCLA educator course (Louise Tellalian's Lecture),  a comparison
of heat vs. cold showed that heat is comforting, increases circulation,
dilates blood vessels and ducts, improves milk flow, relaxes breast
tension and is usually accepted as an intervention. Cold serves as an
analgesic, reduces vascularity, constricts blood vessels and ducts, may
inhibit the MER and maybe culturally taboo. I welcome additional input
on this topic. We need to have some definitive studies done!
Mary Kay Smith, CLE, IBCLC
Romeoville (Chicago area) IL