Reduce color temp a specific amount across all images

I believe latest update includes an easy option to select the entire image for applying 'local' adjustment - this has always been possible (with a graduated filter) but only by manual means. Having a mask for the whole image, one can then apply local adjustment 'as if' global, including White Balance temperature and whatever else.

Local adjustment always works as plus or minus change, regardless of whether it's being applied to a Raw image or to a JPG image (or whatever). Any method which relies on raising or lowering the Basic panel Temp numbers will AFAICT struggle to deal with a mixed set of images - where some express their Temp values as plus / minus, and others as Kelvin degrees. Plus 10 will not produce the same visual change in these cases, furthermore adding (say) 10 produces a different amount of perceptual change, at different points along the Kelvin scale. Local adjustment seems to bypass this difficulty quite well in my experience though especially for WB, the inherent differences of editing from Raw and JPG picture indormation cannot be eliminated. Results will necessarily be merely similar, and less so at the extremes of tone or hue.

With AutoSync one can add such a mask onto many images together or else this can be synced onto those by name (very helpful to name such special purpose masks IMO) after the fact. Or include that mask with its saved adjustment in a user made preset.

This apprach doesn't tinker in any way with the extant (varying across images) Basic Panel settings for Temp etc. Unlike the action of a relative preset, it stays separately updatable or else completely removable leaving everything in Basic just as before. As a bonus: this way you can go on to subtract areas of the picture from receiving this overlaid "relative look", within the Masks panel. 

Have you considered creating a couple of presets that reduce the color temperature at different levels? If one preset doesn't work then you can apply the other one.

Have you tried fine-tuning the Auto white balance option in your camera menu? (Amber-Blue equates to Temp and Magenta-Green equates to Tint)

If all of the photos you take are turning out too warm for your taste, so far as Auto WB is concerned, then you can do something about that directly - affecting both Raw and JPG.

So far as Raw is concerned, whatever modified WB metadata results from this in-camera fine tuning, should then transfer through to Lightroom whenever the photo's set to "As Shot" (though not when you set the photo within LR to any other WB option, including LR's own 'Auto' WB setting.)

There is no way to specify the amount, but Quick Develop's WB buttons work incrementally.