Topless cage? Halogen bulb?

Hi guys! I'm trying to get the heating/ temps correct in my viv and it's not working, roughly ten degrees too cold. I currently use 150watt bulbs from the petstore. His cage is rather tall though (48x18x25 - glass, has slidig doors as well as two seperate screens(brand is MartyMade)). My viv is sitting on a utility shelf, so I was wondering if it would be okay to get ride of the screen top above the basking side and lowering the basking bulb into the cage, keeping a distance of basking platform and the bulb. I already been planning on moving the uvb inside the cage, and would like to move the basking as well to make it warmer. The basking bulb would have to be connected to the bottom of the shelf above it (which only has my stuff animal collection on it). Also would using a halogen flood light bulb keep it warmer than the petstore ones? I've read somewhere about halogen bulbs being bad for their eyes though? I don't want to get anything that could hurt his eyes, he just got over a shed that bothered his eye a bit. I think a major reason why I'm having issues with heating is my mom keeps the house pretty cold, so any ideas on how to insulate the glass would help as well.

TLDR: viv is roughly ten degrees too cold, is it okay to have hanging basking bulb w/o a screen lid? Are halogen flood lights bad for beardie eyes? Would it help to try to insulate the glass/ how?

I leave the top off of mine. The main concern would be other pets gaining access to the cage or your dragon being able to climb out and not get back in. If you don't have other pets around and the climbs are low enough it should be no problem. Just keep the bulb a safe distance above the basking spot (out of reach).

Halogen flood lights work pretty well as basking bulbs. They are similar to the reptile basking bulbs but a bit cheaper. You may need to try a few different wattages to get the correct heat with them. I'd use either a PAR38 or a BR40 indoor flood light if you go that route. You could also configure the basking spot to use multiple, lower wattage bulbs to make the basking area nice and wide. The regular white flood light bulbs shouldn't cause eye problems. Avoid coil bulbs or ones with neodymium coatings - those are the ones that can cause vision problems.

I have a 4x2x2 tank with screen top and we use a 90w halogen for the hot side and a 75w halogen on the cool side for light and added ambient temperature... perhaps add a second lamp?

If his basking area is still too cold you can always raise his basking platform - we use a big rock

edit: oh!! you said a pet-store lamp. We tried those and found them to be way too cold. Returned them and just bought the halogens from the hardware store - cheaper and better It did mean we had to add an additional fluorescent for the UVB though.

Okay thanks for the tips guys!
I removed one of the two screens (the one above the basking area) and bought one of those lamp stands from zoo med and lowered the basking dome into the cage a bit, and now it's a double dome one too so I'll just have to play around to get a mixture of bulbs and desired height to make it the perfect temp. I think I might buy two more lamp stands to lower the uvb, but it depends how to connect the fixture, might be harder. Rheagal is much happier already though with the temperatures! Thanks again 8)