It has definitely been warm in the hoop house, but I just took the ends off so I think the temperature is OK now. Plus, peas produce here into July.
The hoop house was built on top of grass, which was sheet mulched with first a layer of
cardboard, sprinkling of blood meal, uncomposted kitchen scraps,
chicken manure and shaving from the coop, lots of brown leaves and old
straw. All of that sat for about 3 weeks before anything was planted, and when I did sow the seeds they were sown in about a 4 inch trench filled with good potting soil.
I just googled "how to pollinate peas" and came back with lots of links saying peas are self pollinating... so maybe they just need some more wind/agitation?