From some light research

The compost heated greenhouse is not at all a new idea, it seems. Such attempts have been made at least as far back as 30 years in multiple countries. It also seems it is a good idea, as such experiments have been quite successful. 

One reason this is a good idea is that compost produces mostly CO2. Since plants inspirate CO2 and expirate O2, increased CO2 levels in a greenhouse is a good thing. It can boost plant growth and production by as much as 40%! In fact, one problem often seen with winter greenhouses is lack of CO2, as plants absorb the existing ambient CO2. Since winter greenhouses are most often closed to external sources of CO2, the greenhouse is naturally lacking in this gas, which plants require. 

This is in addition to the fact that compost can produce heat up to 140 degrees F (some sources say up to 165 degrees F). Now, much of the research has involved compost heaps much larger than my own. The ones in research were several tons large. So, I'm not sure just how much heat my own puny piles will produce but any amount of heat which helps at least decrease the need for external sources of heat will be welcome.

So, by placing a compost pit or bin inside the greenhouse during winter months, it would seem you are providing multiple benefits to the plants inside. You provide heat and CO2 at the same time you are basically cooking them a healthy meal. 

Most of the American research has included manure as a major component of compost. However, European researchers have achieved the same temperature ranges with little or no manure and the end chemical composition is virtually the same. It appears to me the benefit of manure is simply bacterial introduction. Yet, once the required bacteria are present, they remain present and continue to propagate. The trick is simple. Never completely empty your compost pile. Always keep some back for the next batch, which transfers the bacteria along. It's like making sourdough bread starter. I've been doing this since my first compost batch and it has proven to work.

Some research has included using compost to heat water and has worked well. Once again, the compost heaps were considerable and required heavy equipment to manipulate. I don't have the money, the equipment or even the available material for such a large compost heap. I kind of question the practicality of such a thing, if you need large machines, any way. They also included pipes and pumps to circulate the water. My thinking is that simple small, slow fans over the pit would help oxygenate it, possibly increasing heat production even more, distribute the heat and the CO2 more effectively. (If it can be solar powered, even better!)

So, I'll place several pits or bins inside the greenhouse over the winter. Get a few thermometers and at least one temperature probe to check and record progress.