Unless you know this guy very well I would walk away from a 350 which has been bored .060. To me that shows that the engine has already had at least two rebuilds or that it really was run hard prior to this to need a .060 bore to clean up the cylinders. I do not know how much the guy is asking but running 350 small blocks can be found almost anywhere and you can always get a rebuilt one from a reputable rebuilder for about $1,000 plus core charge.
As to the cooling issue it would depend on what you going to put it in. A 350 in an Advance design truck could have cooling issues unless the radiator is upgraded and/or fans are added. HD radiators for AD series trucks start at about $350 plus shipping. Task force trucks came with small blocks so their original cooling systems should be able to handle a 350 unless you are really tricking it out. There are several radiator options you can use for a task force series truck as space constraints are not as bad as AD series trucks.