Does Increasing ICE Engine Efficiency Lower Exhaust Temperatures Proportionally?

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So the current estimate is that an ICE engine is about 20%. If we were able to increase the efficiency of a given engine, would that result in a proportional decrease in exhaust temperatures? (Given that driveline loss to friction is constant)
 
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It would depend on how the increase was achieved. An ICE emits waste energy not only through the exhaust but also though the radiator and directly to the air. If the efficiency increases, the decreased emission of waste energy could be in the form of reduced exhaust temperature, reduced exhaust volume, reduced heating of air via the radiator, reduced heating of air via circulation through the engine compartment, reduced noise or vibration, or most likely several of the above.