I've always worked on the premise that ice is only really beneficial for the first 36 hours after an injury, to prevent immediate swelling as much as possible, and also just after each run in the case of ongoing problems like shin pain.
Both the physios I've used in the last couple of years said that ice wouldn't make any difference for an injury that was more than a few days old, and that the best way to encourage healing after that was heat, as it it increases the blood flow to the injured area which speeds up the healing process.
Not 100% sure this is correct, just what I've been told.
P.S.
at the thought of the corn weevils...