How did you do in the temp job? Did you talk about the posibility of joining full time while you were there / when you were leaving?
If you've emailed the kind of person who is always busy then its not really surprising that they haven't emailed you back since you haven't really asked them for anything, you've just informed them your going to be applying, and as you've said, at a big company with an online application process, there's probably nothing they had to say about it other than 'okay'. Alot of people wont actually bother emailing you back just to say that they will support your application and all the stuff you were thinking, unless you actually ASK them to?
I dont know your old manager, but if i emailed someone about an application and they didn't reply, i would feel abit weird, but then, i'm the type of person that would actually ask straight up if they would support my application and if they could help me get the roll, which is why i originally asked how your temp time went, would this manager likely want to support your application?