If the turbocharger is producing > 0.5bar or 8 pounds of boost, then you need an intercooler (radiator) to reduce the temperature of the intake air charge down enough that the air density is closer to ambient temps, otherwise you totally defeat the purpose of the turbocharger > cramming more air molecules into the combustion chamber without increasing displacement.
Below 8 psi, there is not enough increase in air temp post turbo to warrant the use or expense of an intercooler, but once the boost is over 8 psi you'll need an intercooler to reduce the compressed air temperature to take advantage of the boost.
A turbocompressor is usually around 65-75% efficient and at about 1 bar or 15 psi the compressed air temperature is around 300 - 350 degrees Fahrenheit, which needs to be lowered with the use of an intercooler to somewhere down around 140-160 degrees F. in order to make use of the compressed air adequately.
Remember, compressing air creates hot air, hot air is less dense.