^Adding to the above, Barry Goldwater in 1964, Richard Nixon in 1968 (and in 1972), and Ronald Reagan in 1980 almost certainly won Thurmond 1948 voters, particularly since all three of these Republicans were endorsed by Thurmond himself. Thurmond's influence helped to decide South Carolina in those years, particularly in 1968, when Nixon prevailed by a narrow margin over George Wallace. In 1976 of course, South Carolina went by 13% for Jimmy Carter, although Thurmond endorsed and campaigned for Gerald Ford. It's possible that Ford still won a majority of living Thurmond 1948 voters, but my guess is that Carter cut deeply into them-of course, his overall margin of victory was provided by blacks. Most living Thurmond 1948 voters in Georgia, on the other hand, probably went for their native son Carter.
I am not totally sure that Nixon won Thurmond voters in 1968 considering that George Wallace destroyed him among White voters in Mississippi, Alabama and Louisiana - three states where Thurmond swept in 1948 as he was put on the ballot as the official Democratic candidate (and which collectively had roughly half of the total national votes for Strom).