If you want to represent a one-dimensional gradient where what is most important is "hot vs cold", i.e. the extremes, then you shouldn't be using a colormap (rainbow) in the first place, you should be using a direct gradient instead, whether grayscale or interpolated between two nearby colors (e.g. red/yellow).
Colormaps are for where highlighting local variation is important -- more important than indicating whether something is closer to one extreme or another. In the examples, this means being able to distinguish the patterns of the objects. In math plots, it means helping to see the shapes of curves. In weather maps, that means judging variation within your state, even while the map ranges from Alaska to Florida.
For this, it's most important to be able to maximize contrast in local differences but also have the perceptual rate of change be roughly comparable.
Rainbows maximize contrast using hue, because our eyes can simply distinguish so much more than with just brightness. Turbo makes the rate of change more constant than Jet. And Jet/Turbo most importantly double the resolution that Inferno has, going from dark-bright-dark rather than just dark-bright.