Cold baby hands

First let me say I live in New England and it’s been extremely cold out at night, we keep our heat between 69-71 degrees, but our room is above the garage so it gets a bit chilly sometimes, especially at night. We also run a space heater until we go to bed. My son is almost 5 months and is still sleeping in our room and lately his hands have been freezing at night. We layer him up and he sleeps in a fleece long sleeve sleep sack, we try to keep his hands as covered as possible but he likes to suck on his hands so his sleeves get wet and I think that makes him colder. He wears 6 month pajamas so they don’t have the foldable hand covers. Is there anything I can do to keep his poor little hands warm at night??