In my experience, the heat shouldn't be a problem. The chain is long enough to keep the paracord far enough away. Another option to help with heat/light distribution is the "pack flat" reflector accessory you can purchase. I really like that one.

Those little lanterns are really great. I recommend keeping one with you whenever you head to the woods. I am heading out this weekend with my scouts and am brining mine along. I have not done this in the past, but may try it out in the tent to take the edge off the cold.

Enjoy!