Wow, sorry for being so late in answering this.

It's necessary to answer this first by distinguishing the Nixon we'd be looking at in 1952-1953 (so pre-Vice President into Vice President year), and the Nixon Kimball is portraying (President Nixon).

Younger Nixon was a bit more hawkish when it came to atomic weapons. It's very important to keep in mind that when Eisenhower came in to office, there was a pressing sense of urgency toward reevaluating the purpose and use of atomic weapons. This is one of the reasons Project Solarium came into being, but the use of atomic/nuclear weaponry was something Eisenhower, Dulles, and Nixon argued about rather consistently throughout the administration. I tend to agree more with the position that Eisenhower really didn't see any issue with his standpoint that if the United States entered into a war it would treat nuclear weapons like bullets, they'd be used often and freely. Some (Campbell Craig) argue that Eisenhower simply pushed this line in order to cow those who advocated freer use of nuclear weaponry, since Eisenhower always suspected that if the U.S. used such weapons, the Soviets would too, and there'd inevitably some kind of war between the two, nuclear holocaust etc.

This is a very brief, albeit roundabout way of stating that I believe Eisenhower's threats to use atomic weapons in the event of renewed hostilities in Korea was not a bluff or a mere psychological ploy - and Nixon almost certainly did not think it was a bluff at the time. Almost certainly by the time he examined things years later, say by the time he wrote Six Crises and backhandedly complimented Eisenhower as "far more complex and devious…than most people realized" Nixon came to believe Eisenhower had duped other states with his and JFD's often quick resort to threats of nuclear attack.

The other issue is that post-armistice, the Eisenhower administration was very clear that if the communist side renewed hostilities in Korea, the U.S. would attack Soviet positions with atomic weapons (see FRUS, Korea Part 2, pages 1193-1198ish).

I think what I'm actually getting at here is that I disagree with Kimball's assertion that Eisenhower's handling of the Korean War can accurately be described as even a proto-form of the Madman Theory or really serve as inspiration for it in any but the most indirect manner. The problem is that I'm convinced of the opposite position - I believe Eisenhower would have used atomic weapons against North Korea, China, and the Soviet Union (in that order) if the war in Korea was not halted, escalated, or was renewed by the communist forces. I'm not convinced it was a bluff.

I'm sorry, this really doesn't answer your actual question. Again, understanding that there were wider implications, Nixon generally thought Eisenhower's handling of the ending of the war was done well, but that he failed to capitalise in a number of ways on the post-war instability in the region. Syngman Rhee/Rhee Syngman and Chiang Kai-Shek/Jiang Jieshi were both viewed sympathetically by hawks in the U.S. (and obviously by some members of related communities), but Eisenhower viewed both men as destabilising revanchists who might sacrifice global security for their own egos. Indeed, both men threatened to re-invade their respective claimed territories. Rhee offered to serve as a kind of loose cannon proxy, and Nixon in particular liked the idea. Eisenhower and Dulles (and others) were so concerned with the actual effects of Rhee's threats, that when Nixon was sent to South Korea in 1953, he was eventually informed he needed to get Rhee to agree that South Korea would not initiate any hostilities. What Nixon was not informed of (though he was aware of the general plan), was that if Rhee failed to comply, Eisenhower would activate Operation EVER READY, which would remove Rhee from power and replace him with a more cooperative member of the South Korean military, or possibly a junta. Nixon got something like what was wanted, and the Operation never went forward.

But President Nixon and post-President Nixon came to view Korea as a kind of proto-peace-with-honor situation, and thus viewed Eisenhower's handling of it in a far more positive light than the younger Nixon might have.

I'll also cite Nixon's memoirs (RN), and the meeting minutes from the 172nd meeting of the NSC in 1953...which you might be able to find online but can definitely find in Box 5 of the Ann Whitman File's NSC series at the Eisenhower Library in Abilene, Kansas...handy that.