"Can I set them out in the morning (around 40 degrees) in the shade, leave them all day, and then bring them in at nights?"

I have never done that but I wouldn't hesitate. I have grown pansies before and know that they need cool weather to flower. If your artificial light included enough blue light, I would put them in full sunlight.

"It that too much cool weather too quickly?"

I doubt it.

"If I do that will the warmer inside temps at night hurt them? "

I doubt it except it may prevent them from flowering.

"Should I wait until midday when temps are around 55 - 65?"

I doubt it.

"Night time temps are still near freezing."

I would leave just one pansy outside just to find out what happens. If I had to bet, I would bet that nothing bad happens.

Pansies like snapdragons are tender perennials and near freezing or even a couple degrees of frost won't hurt them. Both are similar in that both are frost hardy and both both like cool temperatures. I start my snapdragons inside under lights and then move them to my greenhouse. The greenhouse is mostly sun heated during the day and I have a heater that keeps it just above freezing. The snaps do fine.

A few years ago I had extra snaps--I usually plant too many and it crowds the greenhouse. I don't like throwing them away either. I felt the ground in my south facing flower bed and it was warmish. We had about the temps you describe. I decided to set out the extras and see what happened. They didn't die but grew slowly and were about half the size of the ones grown in the greenhouse at planting time. However once the warmer weather hit they soon caught up to the rest.

I'm not advocating planting now. I said all this to show you that your pansies are not a plant that has to be coddled. I don't think any harm will come to them by moving them outside in the day and inside at night.