Roast corn until tender and brown in spots, turning occasionally, about 40 mins. Remove corn from oven. Toss mushrooms with chopped thyme and 1 tbsp. Sprinkle with salt and pepper. Roast mushrooms until tender and beginning to turn golden, stirring once, about 15 mins.
Cut corn kernels off cobs.
Blend until almost smooth. Set corn puree aside. Heat remaining 2 tbsp. Add rice and stir 3 mins. Add wine and stir until liquid is absorbed, about 2 mins.