Can a stock ford aod handle a 351?

...just because the motor is bigger doesnt neccesarily mean it has more HP, it depends on what kind of vehicle the 351 was in (car or truck) if the HP differences are no more than 150HP over your old one (which I dont think it will be) then you are fine, and I think every transmission should have a cooler attached to it seeing as how their so expensive to replace, hope this helps