Cold Air helps car perform better because its more dense.Dense air in short means more oxygen molecules in the engine which means better combustion which = MORE POWER.
Now a Turbo as we know compresses the air.When the air is compressed it becomes hot. (hot air = scattered oxygen molecules = less oxygen molecules in combustion processes compared to dense air = LESS POWER.
So to overcome this power loss (hot air issue) caused by the turbo (compression of air) there is this "TURBO INTER COOLER" placed before the intake manifold.So before the hot compressed air goes into the engine it is exposed to cool air outside (not directly through some heat absorbing metal,like fins on Indian bikes engines) & allowed to cool a bit making it dense again & then entered into the engine for combustion.
A turbocharger in simple terms, sends more air into engine for better combustion. It works with the help of a Turbine, which is actually a fan, that is rotated by exhaust gases. This helps the turbine to draw in more oxygen. A turbo's speed is about 150000 RPM.
An intercooler acts as an intake to draw air. It is used to cut down the heat of intake air. As long as the temperature of intake air is lower, the density would be high.
Almost all turbocharged cars are intercooled. In india, looking at cars, swift, ritz, indica tdi as well as indigo tdi, vista qudrajet, scorpio, xylo, octavia, verna, safari, punto, i10, i20, older accent. MB, 320d, Commercial vehicles such as the 1613, etc all are intercooled. The tavera is NOT intercooled.
Intercooler cools the temp. of the incoming air into the manifold. Compression of air by compressor heats up the air, and expands it [ adiabatic expansion]. this expanded hot air is not a good source of O2 for the engine. so the intercooler cools the air, making it denser in the process. This increases engine performance.
Intercoolers are of mainly two types.
Air to Air.
Air to Water.
All the above mentioned cars use air to air intercoolers.
To get that Rush of turbos, u need to have a positive boost in the intake manifold. At idle, the indigo turbo doesnt have enough speed to get a positive boost.And this causes the car to be sluggish at initial pickup. However turbo starts compressing air right from 1k rpm and you'll get full boost at 1.8k rpm. But this boost is limited till 3k rpm only. The BOV openes above 3k rpm to avoid damage to engine due to extensive pressure generated by turbo charger and here turbo presure ends. But At 3k rpm at fifth gear, u'll b doing about 130.