Not an option for everyone, I know, but the best compost I have made was by layering 1.straw, 2.fresh horse manure, 3.kitchen vegetable waste/herbaceous weeds/grass-cuttings etc. then made it moist but not too wet - the heat and the quality of compost was amazing. The advantage of getting it really hot is not just that it increases the speed of compost production, but it also kills off seeds and perennial roots and rhizomes. The advantage of straw is that it provides much needed aeration to the heap. The answer, of course, is to turn it regularly, but it is a lot of work if you gave a good sized heap (which is what you need to get good heat).
I have recently been taking advantage of a good supply of well rotted horse manure-on-shavings and I have been too lazy to source some straw (hard to find the more manageable small bales). Consequently, the heap is rotting only slowly and the only real heat comes from hot-spots of grass cuttings. It really needs turning......and some OH pee!!
Just as an aside - I have to be careful when I turn the heap - we have Slow Worms in it. They are so so beautiful - not worms of course, but legless lizards.