I like the warm color if that is the mood you are creating. I find that just about the whole top edge of the perch needs to be toned down to get rid of the blown areas there.
I'm glad to have your opinion, but this is reality. The background is brown winter leaves and white-throated sparrows are that warm brown color. I went back to the master TIFF file and deleted a layer containing a warming filter, but I could see no difference when it was gone. It is a warm-colored bird against a warm colored background. What would you do to fix it? I just inserted a color balance layer and shifted yellow to cyan, red to blue. That cooled it down, but is it nearer reality? I can't be sure. It's a matter of preference isn't it? Verdict from two observers: Unbelievably warm. I'll take it under advisement; and thanks for your input.
You'll find that matters of color and cast are largely subjective. I do a test on almost all of my images to see how close to "neutral" they are. Just because an image isn't neutral doens't mean it is wrong either. I just like to know what I am starting with and then decide whether or not to change it.
I learned the adjustment from Chas (Charles Glatzer) on another forum. Here is what I did:
Open the image, then duplicate the BG layer. On that layer select Filter > Blur > Average. The layer will turn to a solid color that will give you an idea how warm or cool the color temp is.
To that layer add a Levels Adjustment layer and select the center, gray, eyedropper. Click on the now solid color layer, it will turn neutral gray.
Turn off the visibility of the solid layer to see the result. Sometimes that's it, but other times call for a reduction of the opacity of the Levels Adjustment Layer to taste. In this case, I dropped it to 43%.
A little more work needs to be done on the image I came up with, but it is a start. However, like I originally said; I like the original warm version, as long as that is what you meant to come up with.
I confess I like your background better than mine, but like my bird better than yours, mostly because that's its color. The contrast between the warm bird and cool (er) background would suit me better, I think. Your editing routine is beyond my skills, but I may give it a try if I can find the time.
You could add a layer mask and reverse the effect of the change on the bird by painting in black. I thought layer masks were above my head until I finally read a book that made them click (and they had been covered in several). That book was Photoshop for Nature Photographers: A Workshop in a Book
As for the adjustment. not much skill involved as it is just rote step by step unit you get to the choice on how far to decrease the opacity, and that's just a matter of taste.
If there are any steps in my description that you don't know where to find the buttons for or anything, just let us know and someone will post screens shots or whatever.