Tucking blankets not swaddling, is it safe ?

My baby is coming on 3 months old & I have done mostly co-sleeping, but especially as she gets older and is becoming more active I have been trying to move her to sleeping in her crib. I want to be sure she’s warm enough in there, but not too warm ! my bedroom window has a bad draft & it gets cold at night. I have her in a fleece sleep sack & want to put a muslin blanket over top tucked in below her arms for a little extra warmth. Is that safe? Whenever I try and swaddle her she wakes up while transferring to crib.

Edit: I feel like it’s important to state that I do follow safe sleep when I co-sleep & don’t have loose blankets over her in my bed. Or any loose items or pillow. She just sleeps in her sleep sack, not swaddled. I know she’s warmer next to me with my body heat, I think that’s why I’m worried about her being too cold in her crib.