Ugh ... turbos are powered through exhaust gases. Thus, the air coming out of the turbo is hot because it is exhaust gas. Then the hot air flows into the intercooler to cool the air before re-entering the intake stream.
You need to look up how turbo's work because that is so wrong. In particular:
the air coming out of the turbo is hot because it is exhaust gas
Do you really think that burnt exhaust gas at over 1000F with very little O2 left is getting sent back into the intake? Thats just silly. Its not going to burn very well without Oxygen left.
This is a simple version of how it works:
1. Hot pressurized exhaust spins turbine wheel
2. Turbine wheel is attached to turbo shaft which spins in bearings very fast (~100,000rpm) and is lubricated and cooled by oil and posible cooled by coolant.
3. Turbo shaft spins compressor wheel which compresses air. By basic laws of nature the air is heated up when it is compressed.
4 (optional) cool pressurized air with inter(after)cooler.
OT intercoolers in between two turbo chargers were also used on big diesel trucks.
Also air to air intercooler will not cool below ambient, even if you are moving very fast. The wind chill factor is a really heat flux factor. Human dont feel heat, they feel heat flux. Thats why in a 70 degree room steel feels cool but wood doesnt. Your skin has better conduction and a higher heat flux to the metal than the wood.
Looking at a wind chill chart, it says at 20 degrees F and 35 mph it feels like 0 degrees F. What they are saying is the rate of heat flux through human skin is equal at (0 F, 0 mph) and (20 degrees F, 35 mph). So you will cool to that 20F faster if it is windy, but you will never go below that 20F even if the wind chill is at 0F.
Same thing with an air/air IC. If it is 20 degrees out and you drive at 100mph you will have the potential for a lot more heat flux than driving at 10 mph. But because heat flux is proportional to temperature difference you will never get below ambient (20F). When you approach ambient (20F), the delta T will go to 0 so you heat flux will go to 0, and you will get no more cooling.
That is why an intercooler on a N/A is useless. If its placed to get cool ambient air, then you should just remove the IC and place your air filter in that location. Also the IC plus piping adds weight and a pressure drop.