Welcome to NGA,
@em_ev !
I'm wondering if you are actually asking this question because you want to provide heat to the hoop house from the compost, or do you want to use the hoop house to allow your compost pile to keep working throughout the winter? In zone 5a I don't think the compost pile would provide enough heat to grow anything that probably couldn't be grown/overwintered in the HH without the compost pile (unless, perhaps, you were using something like fresh horse manure as someone suggested). It might be more useful to just bury heating cables under your planting beds, if you want to go that route.
On the other hand, if you want to use the HH to give your compost pile a better chance to decompose over the winter, I think that would work pretty well even without the heat cables, as long as you made sure there was enough moisture in the pile throughout the winter. On a sunny winter day the temp in my HH is often 70F and above, compared to say, 20F outdoors.
