I'll bet you that sliding door has an R-factor of about 3, at the most..
Since it's big, that adds up to a lot of heat loss.
I'm pretty sure I can add film to my slider, without effecting it's operation.
The reasons I don't want to put in on the right side, is the handle is there.
And, I'll be grabbing the plastic every time I reach for the handle..
The other reason is the view will be affected by the plastic..
Might be a good Sunday DIY project..