I think I posted the link below before, and its probably a bit late if you already have your hood installed, but the location of the make up air can be of great assistance in not wasting your A/C, and help keep from pulling the outside air in. In a very small space, the examples are not as applicable. I think the rear discharge back supply is probably the most effective, as using an air curtain type return air on the hood itself is too disruptive to the air flow around the burners. Here's a link to the site: http://www.fishnick.com/ventilation/designguides/
The different make up air approaches are in the design guide 2.
As far as a fan is concerned for the window I'd recommend a cross flow fan, you can google 12V cross flow fan and find a lot of hits. They are quiet small and will help on a small service window type application.
Hope this helps.