3 7/16" bore was a size that some guys ran back in the day (that's .250 over), but I can't believe that any of them lived very long.
Maybe that big. That was also when a complete full stroker kit was $129.00 and good (if not new) blocks were a dime a dozen. Be safe today and bore no larger than .125 over. That will give you enough meat for two more bore jobs in the future. Add a 4" crank and you got 276. Not too shaby for a lunk of pig iron, ey?
I've run 70 year old corroded blocks .125" over with nary a cooling problem. Seems unusual that a fresh block would overheat - regardless of overbore. I'd suspect something else normally... Had considered going 3-3/8 on my French lump, but in the end, will likely go .125" over only - simply for multiple rebuilds (should it be necessary)...with the 4-1/8" crank, I can settle for 284"