Prepare a large bowl of ice water. Set aside.
Bring a large pot of salted water to a boil. Add the green beans and cook for 4 to 5 minutes, until crisp-tender. Drain the green beans, then submerge them in the ice water for 2 to 3 minutes.
In a large nonstick skillet, heat the olive oil over medium-high heat. Add the mushrooms, onion, and garlic and cook, stirring occasionally, until the mushrooms are nicely browned, about 10 to 11 minutes. Add the wine and cook for 1 minute.
Add the green beans and thyme and cook until heated through. When done, remove from the heat, add the butter, and toss to combine. Season to taste with salt and pepper. Serve warm.