I recall reading where someone did testing with a home-made airbox feed with cold air, and measured 40 degree F reduction in intake temp post aftercooler!

Even of that is extreme case and doesn't represent potential most could see, it proves the point that cooler in = cooler out.

Compressing air a given amount with a given compressor, with its inherent efficiencies, will raise its temperature a certain amount. If the air is hotter or cooler to begin with, it will still raise it from what it was by that certain amount (within limits of course). So cooler in = cooler out.

Likewise, an aftercooler, water or air based, will lower the temp a certain amount, based on many factors. But if the only factor that changes is how hot the air entering is,its going to lower it BY a set amount, not TO a set amount.