Build a mediom- hot fire in a charcoal grill, or heat a gas grill to high. Rub corn with 1 Tbsp. oil. Grill,turning frequently, until corn is charred and heated through, 10-12 minutes. Remove from grill,; when cool enough to handle , cut kernels from cobs and transfer to a large bowl. DO AHEAD: Corn can be made 3 hours ahead. Let stand at room temperature.
Place onion in a strainer and rinse with cold water to mellow its flavor. Drain well. Mix onion, remaining 5 Tnps. oil, tomatoes,basil,1/3 cup lime juice, and thyme into corn. Season to taste with salt,pepper,and more lime juice, if desired. DO AHEAD: Salad can be assembled 1 hou ahead. Let stand at room temperature.
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