A warm engine is an efficient engine. Anything to reduce warmup time will get the engine into its optimal thermal efficiency sooner. On my previous car I had installed a block heater and an oil-to-coolant heat exchanger, in addition to a partial grille block.
Warmer air going into the engine has more energy to extract - though this isn't clearcut in all cases. Past a certain point, the computer will start pulling ignition timing to protect against knock. Also, this will not help nearly as much with CVTs as with manuals or conventional automatics, as a CVT can often just spin the engine more slowly, and might actually be more efficient with a cooler, denser charge.
Any accessories that run on the engine are parasitic losses. Some are unavailable, such as the oil and water pump - although I have installed pulleys that slightly under-drive water pumps before. Toyota has gone beltless on their latest engines. Removing items such as an alternator, A/C, hydraulic power steering, or underdriving the water pump (be careful with this) will increase the percent of energy in the fuel that makes it to the wheels.
Running a thinner oil will reduce parasitic losses.
Increasing EGR can, in some cases, improve efficiency, for similar reasons a warm air intake works.
Using a higher octane fuel, along with extensive tuning, has the possibility to improve efficiency in certain areas of the map - particularly at very low RPM and very high load.
Similarly, a lean burn tune, with ignition timing adjusted to match, can also improve thermal efficiency - for similar reasons that Atkinson cycle or a warm air intake work.
Increasing compression ratio, along with running Atkinson cycle (or similar cycles e.g. Miller) can greatly improve thermal efficiency.
An offset crankshaft can improve thermal efficiency, by improving the portion of combustion pressure pushing down on a piston at an optimal crank angle.
Knife-edging a crankshaft so it cuts through the oil bath more easily can reduce parasitic losses. Similarly, a dry sump also helps (more).
Reducing friction in the engine (e.g.) through thinner or fewer piston rings improves thermal efficiency.
Roller rockers are an improvement over conventional, because they reduce friction.
Fewer cylinders at the same displacement generally improves thermal efficiency, because they have a greater volume to surface area ratio.
Anything to keep heat in the cylinder helps improve efficiency. A ceramic coated piston might help, or shaping the combustion chamber to increase combustion speed.
The holy grail of efficiency is compression ignition on gasoline engines. I'm only aware of Mazda having done this, with their Skyactiv-X engines. Thermal efficiency improvements can be as much as 20-25% (multiplicative, not additive).
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