120°F is the sweet spot between broken blades and whole blades.
There is a lot more than just cooling a blade down in a brine quench (or any quench) with a shallow hardening steel like the 10XX series steels.
If all that mattered was getting a blade cooled fast, quenching in liquid nitrogen would be superb ... but it isn't!
You would think that a cooler bath would prevent boiling and make a faster quench. However, boiling starts the second the blade enters the bath at 1450°F ... long before the blade gets near the 120°F bath temp. The boiling is part of how the blade cools. What we want is to collapse the vapor jacket around the bade as the thin film of water vapor envelopes it. That is what the salt does. I'm not going into how it helps collapse the vapor jacket, just know that it does. The right amount of salt is a 9% brine solution.
In quenching a 10XX steel blade:
First, you have to cool the blade fast enough to miss the pearlite nose at 1000°F in less than 1 second. The water does that (with or without salt).
Next, you have to drop down to 400°F at a reasonable rate, but not too fast. Again, the water does that as it boils around the blade. The percentage of salt controls how large the vapor jacket is and affects the cooling rate.
Finally, you have to go through the austenite to martensite transition between 400°F and 200°F without the blade tearing itself apart. The salt again controls the cooling rate and allows an even cooling without too much stress.
The problem is that the stress of the transformation from soft austenite to glass brittle martensite doesn't happen evenly in the blade. The thicker spine cools slower than the edge. First the edge converts to hard and brittle martensite. As it does this, it expands because martensite is less dense than austenite. The austenite spine is quite rubbery and compresses easily as the edge expands. When the spine converts a moment later it expands and tries to slightly bend the already brittle hard edge. If this happens too suddenly, the edge forms a small crack, which then propagates up the hardening blade to the spine and breaks the blade in half. Even if the crack does not break the blade in half, the blade is ruined.
That split second between the hardened edge and the hardening spine is when the warmer bath helps. It slows the rate just enough to allow a small amount of auto-tempering of the edge to prevent the cracks from forming.