I screen in my porch as a winter sunroom to heat the house. It does a very good job of that because temperature will hit 120F or higher when it's 60-70F outside. All I do to heat the house is open the door between the porch and house. The porch only hits 120 if I close the door because the house is getting too hot.

The problem with my porch as a winter plant room is that it's too hot by day and too cold at night. However if I left the door open day and night it would be OK for some plants. My porch gets nearly full sun and we have lots of winter sunshine. Also my porch is nearly all open to the sun except for a tin roof. It sounds like your porch doesn't get as much sun, you probably have far less open area to let the sun inside, and you get way more cloudy weather. Thus yours would be less likely to overheat.

Covering your porch windows with 6 mil, 4-year, greenhouse poly might well give what you want. But you might need to leave the door open on cold nights and warm sunny days. Mine drops very nearly to outside temperature on cold nights with the door closed.

I'm also winterizing my porch. Actually I am framing the whole thing in and installing lots of windows and screens.

In the winter all the windows will be closed and any other openings will be covered with plastic.

I've been lucky that I have been given lots of free lumber and am recycling doors and windows.

One problem with the porch greenhouse is the same as any greenhouse: Getting too hot in the day, too cold at night.
A way to smooth out the highs and lows is to put things on the porch that will absorb daytime heat and release it at night. Jugs or large containers filled with water, rock / stone, furnishings, etc. can be used as "sun batteries".

My porch is built on a raised concrete pad with a crawlspace underneath. The concrete gets full sun in the Winter and in the evening I can feel the warmth of the pad compared to other concrete surfaces that don't get sun.

Cooling things off in the day can be done by using fans to blow heat into the house (thereby warming house and not wasting collected heat) or by opening a few windows or vents.