A Parakeet does good when covered at night to help trap heat inside the Parakeets cage and it's best to cover the parakeet at night especially during winter even though your house is warm.
The Parakeet will sleep better and be more comfortable if the cage is covered but do allow the Parakeet some air without covering the cage fully and make sure to use something breathable.
Then in the morning when it's time for the Parakeet to wake up you can then gradually remove the cover from the cage a little at a time.
Also make sure to keep the Parakeet in a warm part of your house and do not place them in an unheated garage or building as the Parakeet could freeze to death in the winter.
You should also make sure the Parakeet stays cool in the summertime so during the summer you may not want to cover the cage all the way but covering it a little to create a dark space for the Parakeet would be a good idea.