I'm pretty certain it was done in Photoshop using the "chrome" filter on some text that had a gold-to-dark gradient fill and was warped over an arc.
I'm not sure how you'd recreate that in Illustrator. The only three ideas I have are drawing those swirls in manually with the pen tool, using some different colored lines and the blend tool, or using the gradient mesh tool as Glenn recommends.
Typically, effects like that are done in Photoshop. One way to do something like that is create a background using various filters to get the chrome type effect, then use the text as a clipping mask. Make the dropped text below. Merge the layers together and then warp the text.
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