How to dress baby for cold nights?

For some reason our daughters room will not get warmer than 66 degrees, even if we turn the house thermostat up to 72, her room will not warm up. We close extra doors, make sure the vent is open, etc. we finally accepted the fact that it probably won’t get any warmer, but now I’m paranoid on how to dress her for sleep.

We have been putting her in a fleece body suit with a fleece sleep sack over it, she never seems cold but I just read some articles saying fleece can increase SIDS and now I’m terrified. Is double fleece safe for babies? How would you dress your little one if you were in my position?