Honestly, I don't see an issue with it. I have the same type of viv that you do, and needless to say, I remove the light from the cage when it's covered with fabric because it would be a total fire hazard otherwise. During the end of summer, I wouldn't even turn my beardie's infared light on at night because it gives him nothing but warmth, and my room was naturally the perfect 'cool' temp for a dragon to sleep in. In the winter seasons, I still don't see the big issue with cage covering it if your beardie is sleeping at that time anyways, so long as the cage doesn't dip below about 65F =)
65F is a perfect winter temp for me to sleep in; I keep my apartment at 67, and I've used a temp probe in my beardie's viv and it stays +/- 2deg near that temp at any given time, so I would consider trying that. Unless you have a way of keeping the tank at an appropriate heat during the day, though, I wouldn't recommend daytime cage covering with the type of viv you own.
Also, if not throwing a blanket over the viv, you can always try simply putting a blanket over your sleeping dragon. Sometimes I do that, but I'll leave his infared on over his tree because every now and then he'll get out from under the covers and bask for an hour, then dive back under his towel. My dragon hates the cave I bought him, but the second I throw a towel or blanket in the cage he dives under it and snuggles with it until morning, and rarely peeks his head out. Don't let his glare in the photo tell you otherwise =P
"Mom, I hate you for getting a picture of this. Soooo embarrassing."