The chicken litter shouldn't added until it's "settled down" a bit. If you add it while it's fresh and it gets hot, it can burn your worms. They like manure after it's dry, old and past that "burning" stage.
We keep a heap next to the chicken coop, and dump the litter into that heap. I will periodically raid that heap for my worms after enough time has elapsed.
As for eggs, the shells are great, and I use them, but I do wash them first. After being washed and dried, I then crush them as finely as possible and sprinkle them into my bins. I think they help, but they are very slow to be incorporated into the castings. That doesn't both me because I've crushed them so much.
Someone else will have to answer the issue of the coldness, as I don't know yet!
