Taking the eggs in is definitely in call. As has been stated, pigeons don't normally just abandon their babies, and it's been quite a long time. Maybe for a few minutes, at the most a few hours, but never for a day or more. Please take the eggs inside.
A very quick set up is just to take a plastic container of whatever size and, using a goose-neck lamp, hang the light just over the eggs. What I'd be most worried about is overheating them at this point, so make sure it's quite a distance away.
Here is the temperatures you need to know:
Hatching temp. for eggs in a still-air environment
(meaning that you don't have a fan to circulate the warm air, so in most home-made incubators such as a box with a light in it, it is still-air)
100-102 degrees F. Try to keep it around there and the babies will do fine.
What concerns me is the lack of humidity also. If you have a hydrometer to tell you what the humidity is, try to get it to around 60% for hatching. Just place a warm, moist cloth or a few sponges in the box with the eggs to bring the humidity up.
The parents are not coming back, so unless you can find someone knowledgeable who's willing to hand-feed the babies, it's going to be up to you. If you live within a close vicinity of some of the members here, I know the babies would be in good hands. Newborn pigeons must be fed small, diluted amounts of a good hand-feeding formula made specifically for granivorous baby birds, such as Kaytee Exact, Zupreme Embrace, Lafeber Nutri-Start, Hagen Tropican, etc. Most of these can be purchased at pet stores such as PetSmart.
There are a lot of things to know about hand-feeding baby birds, especially newborns, such as the proper temperature for the hand-feeding formula, the proper preparation of the formula, the proper temperature of the brooder, and the functions of the "crop". If you plan to raise these babies you're going to need a food thermometer, preferably a digital one. This can be used to measure the temperature of the formula. Formula that is too hot can damage a bird's crop and formula that is too cold and cause crop slow-down. Cold food is not likely to be accepted as well, and will, over time, lead to the shut down of the digestive system, which is pretty severe.
Just so you know, in advance, and in case:
Food temperature: 102-107, no higher, not even by a degree. Very minimum is 100. A non-digital thermometer may be as far as 2 or 3 degrees off, which can cost you a bird's life.
Brooder temperature for newborns:
I've found that 90-95 degrees Fahrenheit is the best. A baby should feel quite warm to the touch, not intolerably hot, however. They should not feel at all cold. Adjust as necessary to keep the babies warm.
A good brooder, I find, is a container of any sort (for instance, a 5 or 10 gallon aquarium, a plastic storage bin, etc) with a heating pad on the side of the container rather than the bottom. Lots of paper towels can be added to the bottom. Shred up a few of them to make a soft nest and to ensure the baby has better grip. Splayed leg can occur if a baby has poor grip on its surface.
If you have "Grip Mat", which can be purchased at any hardware store, it is a good way to keep a baby's feet underneath it, though it must be cleaned regularly. It's environmentally friendly, however, as you will soon find you're throwing out tons of paper towels, both at feeding times and in the brooder.
The purpose of the heating pad on the side of the brooder is that the baby is not stuck on the heat if it feels too hot. It can move closer or further away to the heat as needed. They usually know what they want, but a thermometer is your best bet. Get a heating pad that does not turn off after a certain amount of time and is safe with water--read the label carefully. You can probably purchase these at drug stores.
If you end up feeding these little ones and need more information I'm sure the others would be happy to give it. There are tons of methods to use for baby birds but I feel most comfortable with the "baby bottle nipple method" for newborns. Good luck.