I'm keeping my 62 gram baby BP in an 5 gallon plastic tub (kind of small, even for his size but it's the only size that my UTH can even get close to heating to the proper temps) and am having the most difficult time regulating the ambient temperatures and humidity. I'm using a Zoo Med UTH, a ESU thermostat, a digital probe thermometer, a thermometer/hygrometer combo, newspaper substrate, a hide, and a water bowl. The belly heat is on the lower side for both the hot and cold sides (87/86 and 82/81). I keep my house at 70 degrees all day and all night and since getting him, I've increased the temp to 77. I've moved the water bowl so that it's not over the UTH but still the humidity is in the 70s-80s and he is not in shed. I'm not misting at all. The ambient temps are around 75-80. Should I add a lamp? If I need to add a lamp, how do I set it up since I'm using a plastic tub? Get a clamp? And what wattage/type do you recommend? Should a snake feel cold when you pick it up or warm? Sometimes he's warm other times cold... He seems comfortable though. He's active, not frightened, and not shy. I haven't tried feeding him yet, that'll be today or tomorrow and will be the real test. I'm a first time BP owner... HELP

PS: I've ordered a larger UTH and a new thermostat bc this one is a little off so I'm waiting on those to come in, should be in btw Dec 2-7. When they come in, I'm gonna move him to a longer plastic tub that is 8 gallons but is longer, so I can add more hides.

I know these questions mirror other posts and I've tried to apply those responses to my case but I feel like this situation warants a new post and new suggestions. I'm so grateful for any of your advice! Thank you!