Why does coil feel warm?

Yes it’s normal.
Windings with electricity running through them get warm.
Wait till you grab one that’s hotter n hell.
Then there’s a problem.
Heck yea, I burned myself on one. It didn't look hot and I didn't think about it and grabbed it full grip.

Needless to say, it was a goner when it cooled, it was shorted or whatever.

My hand ached all weekend, so now I always check them before I touch them. It could be a frozen winter day on a car with no battery and i still check it and proceed with caution because that really hurt.