Any liquid-cooled car engine has a small device called the thermostat that sits between the engine and the radiator. The thermostat's main job is to allow the engine to heat up quickly, and then to keep the engine at a constant temperature.  It does this by regulating the amount of coolant that flows from the engine through the radiator and back. The thermostat in most cars is about two inches (5 cm) in diameter. Its job is to block the flow of coolant to the radiator until the engine has warmed up. When the engine is cold, the thermostat is "closed" and no coolant flows through the radiator. Once the engine approaches its operating temperature, the thermostat starts to open.  By the time the coolant reaches its target temperature, it will be fully open. By letting the engine warm up as quickly as possible, the thermostat reduces engine wear, deposits and emissions.  The secret of the thermostat lies in the small cylinder located on the engine-side of the device. This cylinder is filled with a wax that begins to melt at perhaps 180 degrees F (different thermostats open at different temperatures, but 180 degrees F is a common temperature). A rod connected to the valve presses into this wax. When the wax melts it expands significantly and pushes the rod out of the cylinder, opening the valve.   The wax happens to expand a good bit more because it is changing from a solid to a liquid in addition to expanding from the heat. This same technique is used in automatic openers for greenhouse vents and skylights.

So, given the explanation above, it is a bit hard to see how any of this really changes anything in your engine since no matter what the target temperature of  your thermostat is, once it it fully open, it cannot allow any more coolant to flow.  The engine will continue to get hotter and hotter until the radiator fan comes on and starts to cool it down.  So if you really want your engine to run cooler, then you need to lower the turn on temperature of the cooling fans.  The stock Corvette comes with a 195° F. thermostat and a fan-on temperature of 200° F..   No matter what thermostat you have - stock or a 178° version, the fan will not come on and pull air through the radiator until the temperature reaches 200°.  So, for a cooler running engine, you need to change your fan turn on temperature to a lower setting.  Mine is set at 190°.  I seldom see temperatures over 200°.  Prior to the changes, I was running in the 210° range.