Yes, it will be intolerably cold. You should wear warm clothes to keep out of the cold, but sometimes, it is too cold even with fire going! Do not camp the wall if you enjoy suffering. As far as I know, around the wall, there are villages where you can lodge in, the price is reasonable and it is safe. Have a good rest in one farmhouse, and go trekking the next day, this would be much easier.

Actually it is better to camp in a group if you wish to do it along the wall. It is not that cold in late summer...however there are lots of mosquitoes and you are well advised to bring repellent, torchlight, mosquito nets, sleeping bag, enough to drink, no sanitation area of course. September is the best month to overnight at Mutianyi - that would be during the Mid-Autumn Festival aka Mooncake Festival. That's where the moon can be viewed most brilliantly. We will probably make plans to do that this year. It rained last year so we didn't get to do that.