Ways to raise ambient temps in a tub?

[Bogertophis]

...If I got a lower (and smaller!) tub would I be able to lower the ambient temp in the room and rely on the UTH more for heating the tub?

It's really hard to keep the necessary warmth in a snake tub/enclosure/or tank if the room itself is cool, as yours is. You might want to consider a wood cabinet
(like from a thrift store perhaps) that the tub would fit inside of for best insulation. It's really important for BPs because they need higher temperatures (+ humidity) than
many other snakes do. It's really best to get all this worked out & tested for a week before you bring a snake home so your snake doesn't get chilled & sick. -oops!