Okay, here's the
heat grabber on builditsolar
And yes, it does require an "open" window, but it's the same deal as with a window A/C unit, except maybe a better fit/sealing than those accordion baffles give. There's also the opportunity to use that shrink film plastic to seal the inside to stop drafts (as well as using the foam fillers where the sashes overlap.)
For a renter, this is possibly a good option, since no modifications are made to the structure, and you CAN take it with you. (assuming using in a new place or whatever.)
If there are storm windows, a variant of this would be to modify the storm window to incorporate the "grabber" and cut the draftiness considerably.
Another idea could use the same ducting through the window, and replace shutters on the house with collectors hung there instead. A little bit intrusive (store the old shutters in attic/basement for replacing later), but a little more "stealth" and more secure than the "grabber" hanging off the windowsill. Heck, in the case of no shutters, this would just look like you added shutters... you could go above and below the window as well for more area (though losing the 'stealth' of shutter mimicry).
If there are adjacent rooms with similar windows, a larger wall collector could go between them, maybe even flowing from one room to the other.
Another "stealth" option would be to make it an awning over the window(s) with the side benefit of shading in the summer. (this is a more intrusive/installed option, maybe more suited to hiding from a HOA than for a renter)