I've been using the beer cooler hack instead of a sous vide machine and I was wondering if water is the only medium I can use to cook in it. I was thinking that I could fill it with oil for a high thermal mass that would use less energy since I'm using a plastic bag to prevent any contact with the food anyway. Also, how important is that plastic bag? Could I use a broth to sous vide in with something pourous holding my meat and seasoning together?
You could use oil, but I don't think it's worth it; realize that you're going to be using additional energy for obtaining, cleaning, and disposal of it.
Regarding using a broth with a porous bag, well, that isn't sous vide. That's more akin to a slow-cooker. The whole point of sous vide is the airtight barrier between food and heat.
Oil does not have a higher thermal mass than water. Ammonia does, but I'd suggest avoiding that. ;)
Sous Vide technically means under pressure / with vacuum. There are a number of compression techniques that don't use heat at all, but these require a chamber sealer and are therefore mostly just seen in proffesional kitchens. Watermelon works really well for this.
As far as putting your meat directly into the cooking solution, this has a serious disadvantage. One of the great aspects of sous vide is that you don't lose the flavor of your meat since it's in the bag. If you put it directly in to the cooking solution, then the flavor will leach in to the water. This probably won't be nearly as good. That said, Thomas Keller uses an immersion circulator to butter poach lobster. So if he's doing it, you'd have a hard time arguing that it is "wrong". Now is that still Sous Vide? That's a semantic argument, the far more interesting question is "how does it taste?" So keep in mind that the broth will leach flavor from whatever you put in there, but give it a try and let us know how it works out.
As another answer mentions, "sous vide" just means "under vacuum" and can apply to techniques like "compressed fruit" which don't even require liquid or cooking. I have used sous vide compression with fresh pineapple spears and Malibu Rum to make Pina Colada Bites.
Not all sous vide appliances use a liquid water bath (with or without an immersion circulator). Indeed there are several steam ovens that are suitable to use for sous vide including at least one that is specifically designed for sous vide cooking - The Chef Touch System.
Also, the Polyscience Immersion Circulator that I own can be used with oil to go as high as 300F/150C (water boils at 212F/100C).
Finally, you can use fluids that will chill below 0F (such as as glycerol-water mixture) for a sous vide superchiller. Superchiller baths are used at The Aviary to craft its ice for "in the rocks" (see video).