Part Load Pumping Losses in an SI Engine
This website page gives a pretty concise explanation about pumping losses in a gasoline engine. Well worth a read.
Changes of Low Load Engine Parameters by Temperature of Mixture
This technical paper goes over the effects of installing a hot air intake onto a test engine driving a small load. For purposes of discussion here, I have considered only the testing temperature of 90 C (194 F). I have not considered the testing temperatures of 140 C (284 F) and 190 C (374 F) because they are a bit higher than is reasonable. I want to save fuel, not bake things.
For 90 C, the paper mentions that pressure inside the intake manifold rises by a small but measurable amount, which supports the pumping loss reduction idea.
However, the pressure rise (about 2%) is a bit less than the 7% reduction in BSFC seen in the paper. The paper further shows a negligible increase in throttle position. I have seen this effect as well on my ScanGauge - whether going up or down inclines, or even on straight and level roadways, the truck's manifold pressure and throttle position do not appear to have noticeably changed. I used to think that HAI gains were solely from lessening pumping losses. The smaller-than-expected pressure rise and the negligible throttle opening do not really support this idea.
The paper also shows warmer air leading to faster combustion rates, and the effect is certainly seen in the graphs at the end of the paper. Combustion peak pressure appears to move leftward from baseline, which is equivalent to advancing ignition timing by a few degress. This makes sense. In fact, the paper goes on to infer that faster combustion rates are the primary factor in HAI gains.
I think that this paper is showing that the resulting gain in fuel economy from installing a HAI is a combination of the two factors. In any case, the gains I've seen are real, and they merit further investigation.
Edit: Hey! That might could explain why MAF-based cars don't really see any sort of improvement using a HAI. Their engine computers might be overcompensating for higher intake temperatures.