Holiding each ear of corn by its pointed end and steadying its stalk end on a cutting board, cut down along the ear with a sharp knife to strip off the kernels, turning the ear with each cut. Alternatively, remove the kernels with a kernel cutter. You will need about 3 1/2 cups corn kernels. Set aside.
In a large nonstick saute pan over medium-high heat, warm half the butter and 1 tablespoons of the olive oil until nearly smoking. Add half the garlic and saute, stirring constantly, 20 to 30 seconds. Add half of the corn and saute, stirring occasionally, until golden and just tender, 3 - 4 minutes. Add half the thyme and green onions and saute for 1 minute more. Season with salt and pepper and transfer to a large bowl, Repeat with the remaining butter, 1 tablespoons of the oil and the remaining garlic, corn, thyme and green onions. Transfer the mixture to the bowl. Let cool to room temperature, stirring occasionally, about 30 minutes.
In another bowl, combine the tomatoes, cheese, the remaining 2 tablespoons oil, salt and pepper and toss gently to mix. Add the tomato mixture, the lime juice and basil to the cooled corn and toss to mix. Taste and adjust the seasonings with salt, pepper and more lime juice. Serve at room temperature.