I don't know much about birds but you might be able to locate the family of the bird by Googling 'lost love bird' and include the name of the town you live in. If they have posted an ad somewhere on the internet or in a newspaper, it might pop up. The people who lost the bird may have also called local shelters to notify them so if you call them too, they might be able to connect you with them.
Another thing you could try is to check with your local vet hospitals and ask them if they have any love birds as patients and maybe this bird belongs to one of their clients.

I'm so glad you brought the bird in where it can be warm and safe. Whatever happens, at least it is safe now.