I certainly can't tell you what to do of course, but with those average temperatures i think they'd be just fine to go out with a reliable heat source. I know 10 days seems pretty young but these little stinkers aren't as fragile as we think. Mine go outside after a 24 hour or so observation period, whether shipped hatched here, with Mama Heating Pad. Chicks I pick up from any other source go out right away, because they've already been housed in a brooder environment and are already eating and drinking. I have found that keeping them under heat lamps - any kind of heat lamp - doesn't do much to encourage faster feathering. They need exposure to a little cool to feather quickly.
Conventional wisdom has us keeping them in a hot-house darn near until we find the first egg in the brooder! Exaggeration, of course, but it does seem strange to me that we get them home, stick them in a box with artificial lights, keep them that way until they are 8 weeks old or so, then slowly allow them to go outside for excursions. They are going to be living outside - why not start them there? Doing that exposes them to things in the soil, air and water (and they'll drink from anything!) in what will become their home environment. There's no need to give them night-lights because they understand natural day/night cycles. They play, explore and eat all day long, and at night they go to sleep all night long. Mama Hens have been raising chicks outdoors in all kinds of weather, allowing them to explore and learn from their earliest days. She doesn't have nightlights under her wings and she certainly isn't sitting on them and warming them all day long, day in and day out.
Those Eco-Glow brooders are a wonderful alternative to the heat lamp way of raising them. But for me there are three major drawbacks: They are open on all sides, allowing for drafts. They are hard - there's no natural "mama softness" about them. And they are expensive. A heating pad draped over a wire frame goes all the way down the sides, and covered with a towel it's soft and comfortable to sleep under and they love to sit on top and snooze or survey their domain. Think of photos you've no doubt seen of chicks sitting on Mama Hen's back or snuggled by her side. They do the same thing with Mama Heating Pad. And when they get spooked, there's a warm, dark comforting place to scoot under and hide. Seems pretty close to natural to me!
https://www.backyardchickens.com/t/956958/mama-heating-pad-in-the-brooder-picture-heavy-update
If you decide to go with a similar setup, you may have to shove them under there a few times - they've never known what Mama Heating Pad is. And expect some adjustment.....chicks and adult chickens don't do change well. The first time they see it they'll run like their hineys are on fire, then they'll get as close and tight together as they can. They'll just stare at it, cheeping frantically and waiting for it to loom up and attack them at any moment. They are mimicking adult behavior - if you put something new in a coop with the adults, they'll have the exact reaction, running, piling and bawwking in protest.
Anything electrical that you put out in the elements needs protection from rain. My setup is out in the run, not in the coop, so it's doubly important for me. Common sense is your best friend when you move or raise chicks outdoors. If your coop is secure from predators and rain, you should be good to go. Good luck!
