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My question is will this be sufficient to cool my 340 with about 350 hp?

Yes IF the cores are not plugged and rodding out is an option for an OE rad but it can weaken the tube walls (alot depends on the care the rad shop guy takes w it) and you'd want a shroud/properly spaced solid steel or MP thermal clutch fan w steel blades (no flex fans),good airflow into the rad, smallest WP pulley you can find/fit, anticav plate

live every 24 hour block of time like it's your last day on earth