Jim, the main thing that turbulence does in the chamber is increase the burn speed and also the completeness of the burn by exposing more of the air/fuel mixture to the flame front.

A quick illustration of the effect: fill two bowls with water and put a drop of red food colouring in each to simulate the flame front, and make one swipe with a spoon through the middle of one bowl. Obviously the one that has turbulence will mix much faster and more completely.

Turbulence in the form of tumble or swirl during the intake stroke aids vapourization and homogenization of the atomized fuel and air, however, the turbulence associated with the squish effect occurs after ignition and is meant to enhance the burn.

I think you're meaning compression heating rather than molecular friction. While there will be a minor effect caused by the extra movement of the molecules because of the turbulence, the vast majority of the temperature increase will be from adiabatic heating.