Would temporarily replacing inner screens with sheets of plex-glass save heating costs?

significant? probably not. You might save what it will cost in the Plexiglas.

This is done, not quite as you describe.

What you describe will be half ass but cheap

To do it right - Take your screens into an old fashion hardware store. The one that has a screen/window repair service in the basement. Ask them to make you storm windows that match the dimensions of the screens. There may also be kits at the Blue, or orange, store to do this yourself. They hardware store may also be able to order you safety glass which will look a lot better.

Plexi glass flexes a lot, scratches easily and will look shabby after a year or two.

I worked for years in a dark basement making and fixing windows and screens at an old fashioned hardware store.

Why don't you just wrap the screens in clear plastic, and stick them back in?

My casement windows don't have a very good seal around the screens, good enough to keep out the bugs but not good enough to prevent air infiltration and water vapor to get past the insert. I think you will find enough air and water vapor will get past to condense and freeze on the outer thermopane glass and cause more problems than you solve.

You would have nothing more than storm windows. It should be fine an reduce heating cost.

You had better take into account the thermal expansion of the plexi if you do this. Due to shading effects, the expansion/contraction may not be uniform either.

I cut the wire out of the screen inserts to some Andersen windows last year, then added shrink film over both sides of the insert frame, then added cheap storm windows, with another layer of shrink film over the storm frame inside the glass, so these windows have 2 layers of glass, then 3 shrink films, then another layer of glass. They've held up well, with glass protecting plastic, and the optical quality is good.

Nick

You want the best air tight seal to be on the inside window, so that moist home air doesn't get between the inner and next pane and cause condensation. This might cause a problem with your idea. I'd try with one window to see if this is a problem.