Air intake
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That's the resonator - the air doesn't really go anywhere, just takes a longer path to the throttle body. A common mod was to cut it at the two outlets and then RTV a circular piece of metal in each hole - the "50 cent mod." That's only for 2008 models - the resonator changed in 2009. 
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If I understand it correctly, the oem resonator, silicon tube mod, and Smart Madness intake all get cooler air to the engine from the driver side "scoop" on the rear fender (451). Any mod with an exposed cone air filter, (i.e. visible from inside the engine bay) is pulling in air heated by the engine. Or at least hotter air because with the resonator removed, the side vent is now scooping air into the engine compartment instead of the intake.
What I don't quite understand; the oem resonator has a longer route to "smooth" throttle response meaning a slight restriction of airflow? I seem to remember that doing away with the resonator doesn't really improve or degrade throttle response, but might make it harsher under some throttle/load conditions? I think the differences are going to be minimal between the methods that pull in air through the fender, as the computer controlled fuel injection/engine management system adjusts itself based on data from the sensors. I am not sure if the system compensates as well for the cone filters in the engine compartment.
In contrast my Kawasaki motorcycle from the 80s has four cylinders with a 32mm carb for each cylinder. All four pull air from a plastic resonator box which only has one intake port that is about the same size as one carb. If you remove the resonator box, the carbs can pull 4x the air and the bike will run so lean it has to be re-jetted to compensate as it has no fuel injection/engine management capable of doing that.
Both the Smart and Kawasaki resonators have internal baffles and a somewhat convoluted air path that seems counter intuitive to me. Presumably these were designed using some sort of air flow dynamics, computer modeling, or some other arcane method. So;
Smart 451 with modified or no resonator using cool air + engine management = no worries?
Smart 451 with modified or no resonator using hot air + engine management = marginally less performance/efficiency?
Both may sound different (throatier) than OEM?
What I don't quite understand; the oem resonator has a longer route to "smooth" throttle response meaning a slight restriction of airflow? I seem to remember that doing away with the resonator doesn't really improve or degrade throttle response, but might make it harsher under some throttle/load conditions? I think the differences are going to be minimal between the methods that pull in air through the fender, as the computer controlled fuel injection/engine management system adjusts itself based on data from the sensors. I am not sure if the system compensates as well for the cone filters in the engine compartment.
In contrast my Kawasaki motorcycle from the 80s has four cylinders with a 32mm carb for each cylinder. All four pull air from a plastic resonator box which only has one intake port that is about the same size as one carb. If you remove the resonator box, the carbs can pull 4x the air and the bike will run so lean it has to be re-jetted to compensate as it has no fuel injection/engine management capable of doing that.
Both the Smart and Kawasaki resonators have internal baffles and a somewhat convoluted air path that seems counter intuitive to me. Presumably these were designed using some sort of air flow dynamics, computer modeling, or some other arcane method. So;
Smart 451 with modified or no resonator using cool air + engine management = no worries?
Smart 451 with modified or no resonator using hot air + engine management = marginally less performance/efficiency?
Both may sound different (throatier) than OEM?
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From a Breathless Performance post in 2008:
"After all the testing we have found that the factory box is a sealed ram air box, which obtains air flow from only the outside (not hot air from the engine bay). Use of a high flow filter proved to out-perform the so-called cold air induction systems. The intake temp on the stock system, with a good high flow filter, was about 10 to 20 degrees cooler then the others thus giving a higher timing curve and optimum fuel mixture and increased Horsepower. This turned out to be an easy and cheap HP increase. Coupled with our .50 cent mod of the silencer part of the airbox removal again increased the HP and reduced 0-60 and 0-80 by over 1 second."
"After all the testing we have found that the factory box is a sealed ram air box, which obtains air flow from only the outside (not hot air from the engine bay). Use of a high flow filter proved to out-perform the so-called cold air induction systems. The intake temp on the stock system, with a good high flow filter, was about 10 to 20 degrees cooler then the others thus giving a higher timing curve and optimum fuel mixture and increased Horsepower. This turned out to be an easy and cheap HP increase. Coupled with our .50 cent mod of the silencer part of the airbox removal again increased the HP and reduced 0-60 and 0-80 by over 1 second."
Three or four years ago, a member did a series of dyno pulls using everything from a stock air intake system to a silicone hose with high performance air filter. I do not remember his screen name, but you can do a search. His best improvement was with the silicone hose and high performance air filter. If I remember correctly, he gained about 5 horsepower. The cold air intake taking in hot engine air was the least effective. I wish I could remember his screen name, but do a search or maybe another member will remember him.
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I think something to keep in mind is the amount of airflow moving about the engine bay and under which scenario you need extra power.
I'll fully admit that an open intake in a stagnant engine bay will cause an increase of intake temps. I argue that once the vehicle is rolling and air is flowing in, around and out of the engine bay that intake temps will be just as low as a sealed air box system.
These Dyno runs are highlighting the stagnant air condition I'm talking about.... Unless the Dyno operator is blowing air directly into that vent in which case I highly doubt you'll see any difference between the two systems.
Tldr: heat soak is only an issue when you're sitting still and can't use the power anyway.
Full disclosure. I bought the injen open air intake.
I'll fully admit that an open intake in a stagnant engine bay will cause an increase of intake temps. I argue that once the vehicle is rolling and air is flowing in, around and out of the engine bay that intake temps will be just as low as a sealed air box system.
These Dyno runs are highlighting the stagnant air condition I'm talking about.... Unless the Dyno operator is blowing air directly into that vent in which case I highly doubt you'll see any difference between the two systems.
Tldr: heat soak is only an issue when you're sitting still and can't use the power anyway.
Full disclosure. I bought the injen open air intake.
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