How warm? warm like ah, that feels nice or warm like not quite ready to put the french fries in yet? Birds have such thin skin and can burn easily. If she got any of the oil into her breathing passages, that could be very serious. With wild birds, the usual procedure is to wash them with Dawn dish soap, rinsing them very thoroughly because they will ingest any soap left on the feathers when preening, then dry them and keep them warm. If you google "hospital cage" you will find some good examples of supportive care.
This is all emergency first aid, which is just a substitute for when you can't get to a vet.But I'd really take my bird to an avian vet if this happened. They have a website, aav.org, where you can search for a certified avian vet near you. A CAV isn't any more expensive than a "regular" vet, but they have a lot of extra training and experience with birds.