I think there have been a few that have successfully raised their temperature through whole foods exclusively, but it seems rare, slower and unnecessary. I don’t think you really need to make a distinction between whole and processed foods; it’s best to simply let your body tell you what it feels like.
As for jumping into refeeding straight away: it depends. If you’re getting strong reactions, then it is likely best to take it slow. If you aren’t, then there’s really no reason why you shouldn’t go at it 100%.