If you are using ACR/Photoshop/Lightroom, it really doesn't matter how you calibrate your display because the profile is used to correct white point and gamma for all your image displays in any color managed apps.
If your print is warmer than you image and soft proof, something else is going on...
Reading your post, adjusting the color temperature of the display would not help - my eyes would accommodate (and so would the soft proofing view)?
Then it must be the viewing conditions. I don't have a daylight balanced viewing light, and it was late at night after a whole day at the computer: warm light bulbs and tired eyes?
The prints look much better in daylight, but I'm not completely sure if I'm getting what I was working towards when I was editing the images.
The other moment is probably the difference of seeing an illuminated picture, like a "color slide", on the monitor, versus a picture that comes from reflected light on a paper surface.
I haven't done a lot of printing yet, so I probably have to develop the feeling how a picture translates from screen to paper.
I'll do an intentionally cooler print and see how I feel about that.