Baby Bird Rescue! The correct way.

A Blue Jay perched on my backyard gate squawked frantically. Nothing unusual, Blue Jays squawk
most of the time, except when they sing, which sounds like a simple flute composition. I grab the garden hose to water my baby vegetables, tomatoes, and flowers. I still heard the Blue Jay and the same bird swooped down to attack one of my cats. A few steps more, and a baby Blue Jay had fallen and suffering in the hot sunshine. I pick it up, seeing it is not responding very well. I carry it a while finishing my watering. 
A basket designated for injured birds is put to use. I place it in there, hang it in the garage to cool down. How long had it been in this awful heat on the ground surrounded by cats?
Later, after a nap, I search on the internet for professional advice on handling baby birds. In the past I had taken them somewhere out of my cat's territory, and wished them luck. Now, the professional bird advice is to put them in something, like a basket, or cut open a large soda pop bottle, place in soft material and nail the nursery onto a tree where mother bird can have her child back safely. So I did, in this terrible hot windy day. Mother bird did notice I think, but the baby Blue Jay did not survive. 
Next day, arrive home about the same time. Birds are frantically screeching. I look over, and I see a baby black bird on the ground, cats hovering, fearing a dive bomb episode from mother bird.
This baby bird is okay. Alert, vocal, and hard to catch. If I could have found that nest yesterday, I would have paid someone to put the bird in it, but, couldn't see it, just heard babies cheeping.
I reach up, place the baby in the pop bottle, but it tumbles out flapping to the ground, I grab it again, cats interested, and just let it go on top the small building under all the trees.
I don't know what happened to the baby, all I can do is let nature take its course.