In a large nonstick skillet, heat the oil and water over medium heat. Add the mushrooms and cook, stirring frequently, until the mushrooms are very tender, about 5 minutes.
In a large bowl, combine the pinto beans, soy sauce, and Worcestershire sauce, and mash with a potato masher. Stir in the mushrooms.
Grate the tempeh on the large holes of a box grater. (Or finely chop it with a knife.) Stir the tempeh into the mushroom mixture until well combined. Shape the mixture into 4 patties.
Spray the broiler pan with nonstick cooking spray. Preheat the broiler. Broil the burgers 4 to 6 inches from the heat for 5 minutes. Turn the burgers over and brush the tops with the chili sauce. Broil for 3 to 5 minutes, or until the burgers are heated through.