Quick question. I have a 4L60E trans. The stock cooling lines into the radiator are 3/8 inch or so, and I just bought a secondary tranny cooler that has 5/16 lines. Is it okay to use this cooler, or does the change in line size cause any problems?

I dont think you'll have a problem considering its only downsizing it 1/16th of an inch... If anything it will probably just slow the amount of oil flow ever so slightly...