Cook the spaghetti al dente according to the package instructions.
In the meantime, fry the grated zucchini in the heated olive oil. Wash and dice the cocktail tomatoes and add to the zucchini together with the thyme. Let simmer for about 5 minutes. Season to taste with salt, pepper and chilli.
Stir everything into the now drained spaghetti and sprinkle with parmesan and serve immediately.