Enclosure without cover/lid

I am looking into getting a bigger enclosure for our growing bearded dragon. Toad Ranch ones are at the top of my list. I have this big nook (currently reading area) in our house where it would fit nicely.

But then I realized that I could turn the whole nook into an enclosure by just putting a glass wall (sliding door) in front. I would need to leave the top open (no lid), and I would be able to hang (heating) lamps over it.

I am not worried about our beardy escaping, and we don't have cats that would be able to jump inside to harass it. What would be some drawbacks about not having a lid/cover? I am kind of worried about the air temperature. Clearly I can set up a nice basking spot, but warm air would not stick around. So the air would likely be mostly around room temperature, around 70 degrees. It is unclear to me if that would be ok.

Thoughts? Recommendations? Thanks a lot!