I don't have a greenhouse, although I want one. I'm going to try to describe an idea, based on post #3. Actual construction details will vary, and the order given is just to describe the unit.
1. Assuming the frame of the greenhouse is in place, but no covering, run a large diameter plastic pipe to a height higher than the roof of the greenhouse. Near the top, several large holes are drilled in the sides, perhaps from near the top down to roof level.
2. Drape a large plastic sheet, large enough to reach at least to the roof of the greenhouse. Secure the plastic to the top using a black, plastic, angled sewer pipe connector. The opening should be on the south side of the greenhouse (assuming . northern hemisphere). Cut a hole in the plastic on the inside of the pipe. Extend the pipe vertically about a foot, Install some sort of chimney rain cap.
3. Build a box on the south side with at least one open side. Paint it black. Run a black sewer pipe from the top of the box to the pipe connector.
4. Finish covering the greenhouse.
The plan is for hot air to rise and accumulate at the peak. The holes allow the air to enter the pipe and exhaust out the top. Air in the black box will heat faster than air in the greenhouse and vent out the top pipe. This warmer air will entrain the air already rising from inside the greenhouse and pull it out the top of the chimney.
Variation: Built the black box and run large diameter black pipe straight up several feet higher than the roof. The top of the black pipe has a reducer. Attach a smaller diameter pipe with an angled connector facing down.The smaller pipe is capped with a large pipe adapter, and then topped with a short length of larger diameter pipe and a rain cap. The top of the greenhouse chimney has a 45° connector and runs pipe over to the black pipe chimney. The purpose of this is to create a venturi to better entrain the air from the greenhouse. Maybe in this case the black chimney is made with ventilation pipe rather than plastic pipe. Maybe the box does not have to be on the south side, but can be at one of the greenhouse ends to avoid blocking light to the greenhouse.
This is just an initial idea, so perhaps people could suggest improvements. After writing this, I imagine someone has done this and described it on the internet or made a YouTube video, but I have not searched for either.
Edit: Maybe with the large diameter black chimney, we can dispense with the peaked greenhouse chimney and just use a top mounted or side mounted exhaust box. Part of the reason for the peaked greenhouse chimney was to provide support.