In your situation, have you considered running it without a battery? I think you would need a 90° micro USB cable. Even then it may not sit flat. If hung from the handle, any usb cord would work.
Running it direct from USB with no battery limits the max output, but should be more than bright enough for a “night light”. There is no excess heat and no battery to cause a problem. Plus it will run forever.
If they made the base out of aluminum it should fix the overheating issue, maybe add a few mild fins to the base as well. Although this would increase the cost.
That’s pretty much the case it seems. It can heat a battery to around 50°C to 55°C. Most cells have an operating range of up to 60°C or 70°C depending on the cell.
After another fishing trip last night where my T1 was half dead before even arriving at the secrete fishing spot cause it got turned on high in my bag I was determined to get TCLO working without use of a paper disk and I accomplished it with ~8” of Teflon pipe tape!