Sib,
You have asked a perfectly legit question, and you have had some poor answers, sorry about that.
The whole airbox thing is very strange as it brings out the tricky subject of who do you believe...the makers who want your money...the buyers who have given them there money and wont ever admit they could be wrong, and the people who just dont know but have a mate etc.etc.
What is clear however is, changing the air intake messes up the engine management ECU settings. If you just look at shape of the airbox on any car, it took someone a long time to make it work as it should in the space available, and working closely with the electronics designer.
So how can anyone come up with a "kit" that fits 90% of all cars and "improves" performance.
IMHO. These induction kits do nothing but increase the intake noise and waste fuel unless you remap the engine ECU to cope with the changes. A lot of people equate noise to speed.
Have you ever seen and heard a Bentley Arnage take off ? A 2.5 ton car 0-60mph in 5.5 sec. and almost zero noise.
Back to your Clio, Rough running on start up is another possible result of removing the makers airbox, and is caused by the AED (Air enrichment device) which is the equivilent of a choke, (found on carburetor cars or the cold start device on early injection engines), malfunctioning.
There is a small precious metal fillament in the air intake tract that detects flow, temperature and air mass. Combined with readings from the water temp sensor and exhaust probes, the ECU sets the AED . When the engine warms up it will switch it off gradually.
Changing the air intake for a so called performance kit, messes this up big time, as does a dirty air filter, the wrong air filter, a leaking air filter box, a blocked air intake, loose clips on the air intake pipes (drilling the airbox) or a combination of all of the above.
If the rough running clears within a few mins and is not severe then some learn to live with it, it can even vary dependant on the outside temp and levels of moisture in the air when you start up.
Another nasty side effect is particles of dust and even grit or stones are able to get into the induction manifold and while it is not something you may become immediately aware of, cause damage or wear to the engine.
Have you never found stone chippings in your airbox and wondered how they got there.
Be careful taking advice from others on this subject, although well intentioned, these people wont put their hands in their pockets if they are wrong, and you blow your motor.
If I went to look at a car for sale and opened the bonnet and saw a cone filter, I would walk.
This whole thing was done 40 years ago with a device called a Peco exhaust extractor which was claimed to give any car a boost in performance and 10% saving in fuel consumption. The streets were full of Morris minors and Ford Anglias wearing them, we must have saved thousands of gallons of 2star at 2/6 a gallon (12.5p)
NOT !!!
Have you ever heard the story about the Kings new clothes ?