well generally my view of efficiency you will get better MPG and power, but if you are loosing one side of the scale you just tipped it you didn't make it more efficient.
lets remember our car were created and tuned in a controlled, possibly indoor, and air condition environment.
ok comparing timing and compression and temperature.
the engine cant make any big differences when it comes to compression vs timing, but when thermal temp is a lot higher there by reducing the amount of air into the combustion chamber suddenly changing the temp to a temperature that isn't too far from itself wont have a bigger impact possibly retarding the timing or making the gas ignite before required to.
if i go on about the CAI I will go off on a calculating tangent
but here I calculated WAI for you
stock intake is about 2 and a half inches wide
air pressure at 70 degrees 100 ft above see level is 0.0742
stock manifold get to about 500 degrees Fahrenheit but lets say light driving you get to 300 and the intake sucks in at 250 (as the temp cools before it hits the IAT sensor {assumeing the IAT is right})
air pressure at 250 degrees 100 ft above see level is 0.0554
(thats what your 2 and a half inch intake opening is getting)
and since pressure cant change in a low volume vacuum the lower 170 degree temperature drop wont make a difference.
except for sparing electronics a bit longer.
but if it sucked air at 170
air pressure at 170 degrees 100 ft above see level is 0.0624
even if you were at see level it will only be 0.0627
all this is still not calculating the humidity in the air as well as the volume.
but if it was added it would look worse due to the quantity of air molecules being less.
but the car wasn't made to have over 150+ degree temp air in the intake.
Im pretty sure sensors go out at extremely hot temps.
and most IAT sensors weren't made for extremely hot air so they might be getting incorrect readings.
which reminds me of if you put a transistor in the IAT plug it will think the air is cold and you will get better mpg a power until the engine blows.
By the way if you want to put hot air into the intake just take the heat shield off the stock manifold it gets everything toasty in the engine bay for you.