Meanwhile, melt butter in a large skillet over medium heat. Add onion and mushrooms; cook and stir until tender, about 5 minutes. Add garlic, thyme, salt and pepper; cook and stir 1 minute more.
Stir in cream; bring to a simmer. Simmer until sauce is slightly thickened, about 5 minutes. Stir in Parmesan cheese.
Drain fettuccine; return to pot. Pour sauce over fettuccine; toss to coat.