I have a sunroom on a 2nd floor with nothing underneath the room to help keep it heated. My worry is that my plants are not going to survive in the room because it gets very cold in the winter even though it is enclosed totally by windows. Somehow I want to keep it warm without having to use a space heater (something that uses alot of electricity). Maybe use solar energy but I don’t know how to set it up.
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Excellent answer above. You need to use thermal mass, so heat is absorbed during the day, and slowly released at night. Masonry floors work best. Ideally, a concrete slab with tile absorbs a good deal of heat. The point is those materials have a low insulation coefficient which may be counter intuitive. But the exterior walls and roof needs to be highly efficient in insulation. And there is the problem, it is easier to design from the get go than retrofit. Also, the roof overhand is important. It depends on your latitude, but the idea is with the proper overhang, the summer sun with a higher declination is blocked. But in the winter with the lower declination, the sun is allowed. But again this is better determined in design rather than as a retrofit.
So some things you can inexpensively do are:
Make sure there are no obstructions, of course. But one is have deciduous trees to the south. Being on the second floor will not make much difference soon, but the idea is deciduous trees block the sun during the summer, but when they lose their leaves during winter allow sun.
Use a dark masonry floor. Use a dark masonry back wall. But also add insulation behind those dark surfaces, so there is minimal heat lose from the materials away from the space you want to heat.
Make sure the ceiling is well insulated, with material that will reflect the heat back in the sunroom.
Hopefully, that will minimize the up and down spike is the ambient temperature. That being said, you may need use some supplemental heat. Although not the purist method, an electric heater on a thermostat used in conjunction with heat sink materials, it will minimize the energy used but still produce a stable temperature.