How to care for a butterfly/moth? Any ideas?

I noticed a lovely butterfly or moth inside the house a few days ago. It’s cold here already. Its colors are beautiful. I left it alone and saw it again perched on a wall and then the next day, I found it on my desk. I tried to move it and it fluttered away.

Later, I found it near the floor and decided to leave it alone (as it was not in an area that gets traffic anyway.)

Today, it was still in the same place near the floor, but apparently in distress. I picked it up and carried it and placed it under a warm spot under my lamp. I have never cared for a butterfly/moth and certainly not as the weather turns cold.

Do I put it outside? Maybe on one of my plants? Do I feed it? I don’t want it to be in distress (if it is). I realize this sounds crazy…but I try to honor all the life in my house (even the spiders) and attempt to find ways to help them along. I have no idea of the lifespan of a butterfly/moth. (I am not sure which it is, because the wings are rounded, not sharp, and it has distinct “eyes” on the wings. Lovely orange and black color.) So, if I sound dim, I apologize, but I’ve never seen something that has butterfly colors, but has a moth’s rounded wings…therefore, not sure what it is.

Any info would be really appreciated. It seems to have closed up its wings and is just sitting quietly under the lamp at the moment.