My budgie chick hatched. Does it need special care or a heat lamp?

If this is a wild bird the best option would be to get it to a wildlife rehabilitator asap. If a pet species you need to know what species in order to feed approriately. You need a hand rearing formula suited to that species. Keep in a "nest" with supplemental heat and humidity as it cannot regulate body temperature yet. Relative humidity greater than 50% is required initially. Hatchlings (no feathers) should be maintained at 95° - 97°F (35° - 36°C). An incubator is usually recommended for hatchlings. The yolk sac should provide nutrition the first 12 or so hours but but it will then need to be fed every 2 hours around the clock Here is some basic info https://vcahospitals.com/know-your-pet/hand-feeding-baby-birds

If your budgie's parents are still around they will most likely care for them on their own. However if the parents aren't around or aren't caring for the babies properly, you will need to start feeding them yourself. Most pet stores will carry a basic baby bird food which has feeding instructions depending on your bird's age. You'll also need a syringe with which to mix and feed the food. As your bird grows you can start introducing an adult balanced diet to encourage them to begin eating more solid foods.

Budgies will typically eat a portion of their own food, and then regurgitate it to the babies so it can be more easily digested by them. If the parents aren't feeding the babies, there are commercial baby bird foods available that when added to water, mix up into a slurry that is easy for the baby bird to digest (since we can't regurgitate to them!). As the babies grow and start to explore on their own, they will begin to eat the regular adult food as well.

Thanks for reaching out about Blue. The average incubation length for budgies is 14-16 days, once she starts sitting on the eggs. A thermostat regulated heat lamp can be used to regulate the temperature. If she is going into and out of the nest box, and has laid egg in the box, she is probably comfortable with the size, as long as it is large enough to rear the young. Regarding nutrition, a wide variety of vegetables and a plant protein source (legumes) is important to replace nutrients lost in laying eggs. Good luck

Momma bird may be a bit stressed out now that there are new babies to care for. Adding in extra food and water dishes so that each bird has one to eat at without fighting, and making sure both birds have their own perches to relax on can help reduce tension. As for the babies, momma bird should care for them herself, however having some commercial baby bird food (most pet stores will carry it) can be useful in case she can't care for them all on her own. As they get a bit older and start to explore, you can start to offer treats and pets to get them used to being handled.

You can clean out the nesting box as needed. Gently scoop the chicks out and place them in a clean temporary box. Expect mom to complain and peck. Scrape the box and fill with clean nesting material. Return the chicks to the box afterwards. If the hen is not feeding them adequately, you will need to supplement​ them or pull them for handraising. Use a commercial handfeeding formula. Follow label directions. If you don't have experience hand feeding, ask your avian veterinarian or an experienced breeder. If this is Boo Boo's first clutch, the loss of some of the chicks may be due to inexperience.

Unfortunately, there isn't much you can do at home if the baby is severely injured or you don't have food for it. Trying to see if a local pet store or big box store that carries pet supplies is open may help you find syringes and baby bird food you need, otherwise. In a pinch, adult bird food can be ground down into a mash and then mixed with water and given via a syringe until you can get actual baby bird food. Keeping the babies warm and keeping any wounds clean and dry can help, however if there are severe wounds or the injuries are bad enough the babies can't function properly, seeking out the care of a vet in person ASAP is best (Many are open still for medical emergencies such as this).