I would suggest a plastic window insulation kit available for around $10 or so at your local big-box home improvement store. Probably also available at your local 800 pound gorilla general store.
It will have double sided tape to adhere to the door around the opening, then the plastic is stuck to the other side of the tape. A hair dryer is used to shrink the plastic until it's taught so you can see through it and that it doesn't flap in the breeze.
The tape probably won't stick very well to that bare, rough wood. At a minimum, you'll also want some sandpaper and some sort of a block to smooth down the wood around the pane so that there's a smooth surface for the tape to stick to. When the door is refurbished, that will need to be sanded anyway, so this is just a head start.
Depending on what's outside, you may consider adding a second layer to the outside of the door, as well. However, the plastic is rather thin and doesn't take well to physical abuse. People, packages, tree limbs, possibly even leaves blowing by, and the wind itself may be enough to tear the plastic or rip it off the wood. But, if you've got plastic left over from doing the inside, it won't hurt to put a layer outside.