Ok- that sounds like what people around here do with a product called "seafoam".
Results can't really be measured without looking at tops of valves with a scope-- and users are usually either pro or con, with no one in the middle. The seafoam does have decent cleaning properties, with some lubrication properties also-- just for most jobs there is another that is better for one or the other.
The "smoke" that you see (I'm not a believer) is simply the product burning-- not excessive carbon buildup.
That said, I've used it myself before storing a car for a few months-- I'll dump some into the combustion chambers to keep them free.
That black box is what you need to remove and clean out-- the air filter housing, and the AFM-- don't remove any electrical components. The entire assembly will lift out after removing the intake boot clamp, and loosening the two 10mm nuts along the (here) drivers' side fender area. There's a flap in this thing, the AFM. Clean out that entire box with cleaner and gently work the flap with your finger or a plastic implement. Don't use a screwdriver, you can damage the walls or flap itself.
The TB & butterfly can also be cleaned out with a shop rag / brake cleaner / toothbrush to remove any gunk present. Just don't spay it liberally into the intake of the TB itself.
If you're experiencing hesitation, it could be related to whether the DME is reading the AFM, or ICV. At idle, (TB butterfly closed fully position) the ICV is active. Off idle, or TB butterfly angle off closed position, the AFM is active.
The AFM has a track inside that can sometimes be a little jacked up with gunk.
A good cleaning like I've described of the entire intake tract SHOULD have noticeable results.
It's not what you buy, it's what you build- Unknown
EN90283 - Stabled for HG repair
DH06247 - Running like a champ