Cook tomatoes and garlic in butter in a 4-quart heavy saucepan over moderately low heat, stirring occasionally, until most of liquid is evaporated, about 5 minutes. Stir together wine and cornstarch in a small bowl, then stir into tomatoes and simmer gently, stirring, 1 minute. Discard garlic. Add Cheddar by handfuls, stirring until completely melted. Serve in a fondue pot set over a flame.
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