A cooler intake air is denser and so more fuel can be burned for the same volume of air. More power results and the thermal load on the engine is reduced - or at least not much increased under higher BMEP and power. That’s the purpose of intercoolers on supercharged and turbocharged engines, but a naturally aspirated engine will also benefit from cooler intake air.
Keeping the exhaust hot will be useful only with an exhaust turbine, because the turbine power depends of the exhaust mass flow, pressure and temperature. Usually the exhaust turbine is coupled to a centrifugal compressor to form a turbocharger. Under high load and revs, the power of the turbine is in excess of the compressor requirement, especially with a gasoline engine, so that there's a waste gate which diverts a part of the exhaust gas to by-pass the turbine. But at low revs, the power of the turbine is insufficient to provide an adequate boost pressure, so any increase of the exhaust temperature will help.
Cheers
Aorangi