Not safe, baby needs to be on a firm surface, make her snuggy with her sleepsuit and sleeping bag 😊
https://www.lullabytrust.org.uk/safer-sleep-advice/mattresses-and-bedding/
You can warm up the mattress with a hot water bottle, leave it in there for 10-15 min, then remove it before you put her down
We put a cellular blanket underneath the mattress so it’s still breathable but felt it stopped some of the draught from where the cot is raised off the floor but otherwise we just use a warmer sleep suit and sleeping bag.
Adding anything to the cot that's not meant to be in there is unsafe. You could add an extra breathable blanket over her sleeping bag X