Obviously, the thermostat will open colder. Whether the engine will actually run cooler or not depends on the condition of the rest of the cooling system.
What year vehicle? I've seen a serious drop in gas mileage on some computer controlled vehicles. As the computer monitors engine temperature, it runs in a "warm up" mode until normal operating temperature is reached. During this "warm-up" mode, the computer is using a little bit different algorithm, which causes the engine to run less efficiently. If the thermostat opens too soon, and the engine never reaches a temperature that the computer deems "normal," the computer will always operate in "warm up" mode, and you can get a drop in gas mileage.
If this is an older, non-computer controlled vehicle, you may not see much if any difference, other than the running temperature.
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