No, the puppies will not be heartworm positive just because their mother or father was. However, having a heartworm positive dog around makes it much more likely that the other dogswill contract a heartworm infection if they are not kept on heartworm preventative regularly (and in the case of puppies started on it early) due to the fact that the heartworm dog serves as a reservoir from which mosquitos pick up infective heartworm larva and then they bite another dog and infect it.