Build a medium-hot fire in a charcoal grill, orheat a gas grill to high. Rub corn with 1 tablespoonoil. Grill, turning frequently, until corn ischarred and heated through, 10-12 minutes.
Remove from grill; when cool enough tohandle, cut kernels from cobs and transferto a large bowl. DO AHEAD: Corn can bemade 3 hours ahead.
Let stand at roomtemperature.
Place onion in a strainer and rinsewith cold water to mellow its flavor.
Drainwell.
Mix onion, remaining 5 tablespoons oil,tomatoes, basil, 1/3 cup lime juice, and thymeinto corn. Season to taste with salt, pepper,and more lime juice, if desired. DO AHEAD:Salad can be assembled 1 hour ahead.