Lets not think gradient and an uth does nothing for your ambient temps.
What you need is a hotspot of 88-90 and the ambient to be around 77-82. Your ambient temp can be the same in the entire tank if it stays in that range. Now an occasional drop to 75 will not be harmful as long as its only occasional and not for a long period of time.
The danger you are facing right now is having a uth that is not controlled. The newspaper is acting as a buffer right now but your snake can very easily go under the paper. Once it does it will likely choose that as its hide. So at that point your snake will be directly on the tank floor and open to being burned by the uth.
It may be beneficial to get a heat lamp of che to use for right now and just provide the proper ambient temps until your tstat arrives. A che or heat bulb can easily provide a hot spot on the hide and proper aired temps alone. A dimmer can be used to get the temps dialed in for that or a lamp stand. Using a lamp stand the closer to the tank the warmer the hotspot and the further away the cooler it will be. Both using distance or a dimmer only works well in a stable climate controlled room. The more temp fluctuation you have the more the hotspot and ambient will change throughout the day and night. To be best controlled a tstat on each heating device is best.
You can cover the sides and back with thick art paper of construction paper which will actually give you 2-3 degrees higher alone. Then what I did to mine was make a cardboard cutout with a heat lamp window. I think covered it with foil and laid it on the screen. This gave me more heat and better humidity control. My room stays at 68 and doing that my 40gallon tank still needed a 100 che hot side and a 60 watt bulb on the cool side paired with a uth. That gives you an idea of what may be needed later when you upgrade sizes.
In the future you may want to upgrade to a thick walled PVC cage but if your like me you may just like how a tank presents itself but know it takes alot to keep it right in a cold room.
I would get rid of the paper water bowl and get a heavier one like a dog bowl, or even a square Tupperware style. The paper bowl is going to be flipped easily.
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