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you engine internal temp is controlled by the thermostat, the ECU, the engine coolant temperature sensor, etc. - it will not run cooler, nor should it.
Operating oil temp is not thermostatically controlled, aside for some setups with external oil coolers where the cooler is bypassed during warmup, or an internal oil warmer which works the opposite until the engine reaches temperature.
Higher oil capacity generally can and will lower oil temps in extreme conditions, but I doubt the difference in filter size is enough.