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Color temperature overrides the light color.
You should be able to change the color temperature of an image with a simple shader network... connect the HDRI image and a Blackbody node to a Multiply node, and use the Multiply node as the Skydome texture.
Physical Sky doesn't need color temperature adjustment, it's already simulating the correct color temperature per sun altitude.
If you need to white balance the camera, you can do it easily in 3ds Max through Exposure Control. In other programs, you can use a Blackbody node as a camera filter map.