My baby keeps waking at night because its cold?

For the last few days my baby wakes up around 2-3am and then starts to roll over and play and also gets up at 7am (usually she sleeps thru till 8ish). I put her in a sleep bag and a couple of blankets on top of her but when i picked her up this morning her arms are so cold (she has a vest and sleepsuit on under the sleep bag. We dont put the heating on as the boiler is in her room and wakes her. I know we need to start putting more layers on her but they say not to do this as babies can overheat? Is there any certain items of clothing out there specifically for nightware to keep them warm and not overheat?