Hi, is there a certain temperature the babies room should be, or does not to matter so long as sleepwear is TOG appropriate? Also, is it safe to have mittens (bonds onsie fold over hands) during sleep? Our 4mo is rolling so is now arms out but his hands are exposed and our home gets very cold. TIA!

Red Nose does not recommend a specific room temperature, rather you dress baby to the room temperature.
Overheating (hyperthermia) can be a risk for babies (as well as hypothermia)
Babies regulate their body temperature via their head & face, so it is important, that baby’s head & face remain uncovered.
If baby is waking & you are concerned that he may be hot or cold (feeling back/tummy or redness of face) then you can remove or add layer of clothing/bedding but still keep head & face uncovered.

Red Nose has the following information.
“Dress baby for sleep and add/remove lightweight blankets to ensure baby’s back or tummy feels comfortably warm to the touch.”
https://rednose.org.au/article/bedding-amount-recommended-for-safe-sleep

“Babies control their temperature predominantly through their head and face. This is why we recommend that you put baby to sleep on their back with head and face uncovered.
Red Nose does not recommend a specific room temperature for baby’s sleep. This is because there is no evidence to show that maintaining a specific room temperature prevents sudden infant death.

As long as baby is put down to sleep on their back, and that baby is dressed appropriately for the room temperature – not overdressed or under dressed – with their head and face uncovered, you can feel reassured that you are protecting baby from overheating.”
https://rednose.org.au/article/how-to-dress-baby-for-sleep

“It is not necessary to monitor the room temperature or to leave the heating or cooling on all night, as long as the baby is dressed appropriately for the room temperature: Dress baby as you would dress yourself – comfortably warm, not hot or cold. A good way to check baby’s temperature is to feel the baby’s back or tummy, which should feel warm (don’t worry if baby’s hands and feet feel cool, this is normal).”
https://rednose.org.au/article/protecting-baby-from-overheating-during-sleep
https://rednose.org.au/article/room-temperature
https://rednose.org.au/article/what-is-a-safe-room-temperature-for-sleeping-baby