Keep the heat on.
If she is congested, I suggest that you also run a vaporizer in her room. We use a Vicks Vaporizer/Humidifier that takes Vicks pads and defuses into the air. It helps my children sleep better when congested, and quiets their cough without having to slime them up with vapo-rub.
It really just sounds like your boyfriend just doesn't want to pay the heat bill - which is understandable as heating a large home is expensive. Keeping the heat off in your home when you have a sick child, or any child, in winter is ridiculous. Your child loses body heat much faster than you - or your boyfriend - does and needs to be kept warm. If this becomes a matter of contention between you and him, take your baby to the doctor and have the doctor tell him the heat needs to be on. If he refuses, you need to take the baby and stay with someone who puts the heat on - especially at night. No, I am not saying you should leave him for good - just get the baby someplace where she can be warm until he decides that the heat should be put on.