I am currently working on a science fair project on composting and what variables can improve the process. I have 4 eight litre piles (3.5 litres carbon products, 3.5 litres nitrogen products, 1 litre of finished compost). The first week the piles were ranging from 15-20 degrees celsius(the temperature around them was approx. 13 degrees celsius). However, after I turned the piles at the end of the first week the temperatures dropped to a range of 15-13 degrees. It has continued to stay like this and the second week is almost over. Most of the veggies are no longer distinguishable and I was expecting the piles to reach the thermophilic stage by now (when the piles really start to heat up,and it is supposed to reach this stage in under a week). The only problems I can think of is the small size(a cubic meter per pile was not possible)or the large amount of liquids in the boxes.
You are correct about the size of the pile affecting the heat. You require a certain mass before it all works. Too much water/not enough air will slow composting down too.