The patio might work, and if it has a south facing wall or even a western exposure, if you slanted the side wall, as in an ‘A’ frame [half of the wall of an ‘A’ frame,] you would capture more sun/heat storage.
The mass of cement would hold heat.
It will work, if you can get enough sunlight.
The Solar Greenhouse books will have mathematical tables to show the angles to get the best sun from the south, for your location. Need I admit that I am not educated enough to use them, so we built as we could and it worked.
About the plastic, if you use the paint drop clothes, they will last 6 months or a little longer and then disintegrate.
They sell a UV light blocked roll of plastic at the Hardware stores, it is going to cost a lot more, but is good for several years.
You could test it with the cheap plastic and if you want it to really work, then buy the proper stuff.
Does the truck driver that posted on TM haul or know someone who installs mobile homes, if so, they use a good grade of plastic to seal the open parts on the mobile homes while moving them, it may not be UV light protected, but would be free , LOL, or for the price of a dinner.
One might even get a lead, by calling a mobile home installing company and asking about the plastic they remove from the mobiles.
If it is in the right spot, you might get enough heat from it in the winter to make it worth buying the good plastic.
The cement floor will be passive storage and a few barrels of water will store even more heat.
And if you are using a cooler in the summer, it will work better in the summer, if it can draw the moisture from the green house.
The first summer we were here, with the roof mounted evaporative cooler, we never got cool, the next summer the 25’ greenhouse was up and a door opened into the house, when the door was open, the house cooled better, with no changes made to the cooler.
Have a good day at work.....Friday’s are nice, no matter what day of the week they fall on.