Question about temperatures

Our nursery is going to be small and has a radiator in it that we plan to turn off. We don’t want the baby to over heat. I know for the first few months they will be with me in the bassinet in our room but just thinking ahead.

We’re turning off the radiator, but it will be winter and cold. Is it okay to dress the baby warm and heat up the mattress pad before putting the baby down? Is it safe to turn off the heat? I don’t want the baby to over heat, but I also don’t want them to freeze ugh.