"It is a warm day" or "I have a full day ahead of me" would be normal things to say in English. But it is pretty odd to put these together this way. Eating a good apple pie on a cold evening might make you feel warm and full.
The sentence is very peculiar, both in English and in Romanian. „A avea o zi plină” means "to have a full day", in that you have a lot to do/are busy the whole day.