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A 327 or 350 (BOTH are 4in bore blocks) will easily go .030 or .040 over. A .060 over is considered the max limit, AND, IT IS ALWAYS RECOMMENDED TO HAVE A SONIC TEST DONE BEFORE GOING TO .060 OVER.
On a .060 over with a blower or nitros, there is a VERY GOOD potential that the extreme pressure in the cylinder could flex the cylinder walls enough to develop a crack.
If the block will safely go to .060 over, then normally aspirated should be fine.
Just been through that with my block 327/300. December 63 casting for my 64 vette ,which is now at 30 thou over, needs boring again we sonic tested it and we have one cylinder with 2.10 mm wall thickness and two with 2.4 mm bores . Don't fall into the trap of just presuming that every 327 will go more than 30 thou over it will end up in tears like me.
JMHO
Don't know if this is an issue w/ Chevy 327, but I bored a Pontiac 400 .60 over and had to go with an oversized aftermarket aluminum rad to keep it running cool.