I do realize that the greenhouse is a closed system. I should have put in the original post, that this would be designed so that the compost is attached to the outside of the greenhouse, and not internal. There are quite a few case studies on using compost heat to run a radiant heat system, but it also makes sense that if you pull too much heat out of the pile, it will stop generating heat because the cycle will have been killed off.

Maybe I'm trying to find the easy way out, but I figured since I have an abundance of cow manure available to me, I could leverage that for some heat.