Hue saturation layer on colorize, and another also on colorize with a slightly yellower color with a soft light blending mode and a low opacity. This brightens the lighter parts and darkens the blacks just a little.
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Used select/color range clicking on one of the lightest parts, then filled selection with white. In the layer styles set a yellow outer glow set to hard light. The layer its self set to overlay.
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Same method, color range selected the darker parts, filled with black but this time set the outer glow to a red color.
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Painted with big soft brush with black and white on a layer set to overlay.
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Masked away part of the wing and started placing bits of fire. All the fire layers are set to either lighten or screen to drop out the black.
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more fire, some in front of the bird layer some behind. used the same flames a couple times each but always transforming and warping and flopping and cutting different pieces to prevent it looking like the same exact couple flames over and over.
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more flames, and started painting in little embers on a few different layers with slightly different outer glows, and inner glows. all obviously orangey yellowish hues. Also used the flying ember source image here.
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forgot to mention the slight use of some render clouds set to overlay and masked away in the last step. Here I started placing in the coals.
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Hue saturation layer set to color rise then turned down a bit to get to coals to match better and not be so red. after this just some finishing touches, more little glowys and some slight blurring to meld everything together better and hint at more depth.