I've just turned my compost heap as it looked to be half rotted and found it does not have any worms. I am mixing lawn clippings, vegetable peelings and garden weeds. It does not seem to get hot enough to decompose egg shells, orange peels or paper. Is this normal or am I doing something wrong? 

• Make sure your compost heap is in a warm sheltered spot away from tree roots that may invade.
• Use a 50/50 mix of green and brown organic material.
• Green material includes vegetable scraps, grass clippings, garden weeds, leaves and animal manure (not cat or dog).
• The brown layer is tree prunings, twigs, shredded paper and cardboard, bark, straw or hay. 
• It sounds like your heap needs more carbon elements, that is twigs, sticks, tree prunings, as you have too much green matter for the heap to heat up. 
• Egg shells won't break down they will crush and that is good enough for the garden. Citrus peel can sometimes take longer to break down. 
• Add in some more layers of cardboard, egg cartons and shredded paper, twigs or similar and sprinkle in Tui Blood & Bone and Dolomite Lime. The blood & bone will stimulate the microbes and get them working, as will dolomite lime, it will start breaking down the organic matter.
• Add a few handfuls of Tui Sheep Pellets or Tui Chicken & Sheep pellets, this will help get the microbes working, generating heat to break down the organic material.
• Cover the compost heap to help generate heat, leave it for 6-8 weeks before turning and aerating.