I’ve been turning it as best I could -
Our muck heap at RDA Dunfermline is never turned. It's just added too. It's in a spare field
When the heap gets too long - we add to the length not the height - we start a new one.
We have a system - 9 horses drop in field, us volunteers lift the heaps daily and put in a wooden slatted three sided uncovered field bin - then our digger empties that to the line in the spare field when it's almost full.
The same system operates in the arena - from arena to three sided container outside, then to spare field
I honestly don't know it's temperature as I don't get too close to it. But the first heap is reduced by anyone who wants it takes some - neighbours, local farmers etc (not enough though so it doesn't go down fast enough

) and when that's sufficiently reduced they'll go onto the next line.
It is pretty dry cold stuff almost like compost from teh shops and doesn't smell
I don't know if that helps you, but I did also wonder if the duck poo has any effect?