Nursery, no air vent.

Hi! I'm due to have my second baby in 10 days. We currently rent a house with 3 bedrooms: one for us, one for our 2 year old daughter, and the third we've set up as a nursery. I think the nursery used to be connected to our daughters room as the master bedroom but was split into two room. My problem is the nursery doesn't have any sort or air vent for heat or AC.

Our baby will initially sleep in a bassinet in our room until she's ready for the crib. I was jsut going to use the nursery to store her stuff and for her to play sometimes because I thought we would be moving out of this hosue before she needed to sleep in the crib but it seems unlikely at this point. Without a vent the nursery gets too cold in winter or too hot in summer when the door is closed. I can’t leave the door open all the time because we also have a toddler, and I can’t rely on the windows since they’re old and don’t have screens, so I can’t keep them open all summer.

During winter, is it safe to use a space heater in the nursery? I’m struggling because I can't fit a crib in our bedroom, and the nursery would be to small to switch with our bedroom —there’s barely enough room for the crib and dresser as it is. What can I do to make the nursery a safe space for the baby?