Preheat a grill to medium-high. In a large pot of boiling, salted water, cook the pasta according to package directions until al dente; drain, reserving 1 cup of the pasta cooking water. Return the pasta to the pot.
Meanwhile, brush the squash pieces with 1/4 cup EVOO and season with salt. Grill, turning once, until nicely charred, about 10 minutes. When cool enough to handle, coarsely chop.
In a large bowl, combine the tomatoes, corn and remaining 2 tbsp. EVOO. Add the ricotta, garlic and thyme; toss well. Add the drained pasta and stir in about 1/2 cup of the reserved pasta cooking water. Season to taste with salt and pepper and add more cooking water as desired.