We are talking 300/500 CL, as the 400 is different.
A) High Flow has nothing to do with temperature, just air volume. Recirc fan likewise just 'recircs' what is there independent of temperature.
B) L Pack controller controls Cockpit temp. There is an excess of supply (think relative volumes) so the excess goes off into the cabin. Thus any changes in temp selection on the left pack WILL have an effect on the cabin temp but a small one, over-ridden by the R Pack setting.
Do you have access to any 737 tech info?