Actually, either of those examples could be considered grammatical, and neither sounds wrong to my ear.
Formally speaking, it should be thanks go, since thanks is a plural noun. If in doubt, just use thanks go and don't worry about it.
However, because thanks is so often used as a fixed expression, more and more people treat it as grammatically singular despite its plural form. For that reason, it's not uncommon to hear thanks goes, and this usage sounds natural to me.
Interestingly Google shows 1.9 million results for "thanks go" and 3.5 million results for "thanks goes", suggesting that the latter is actually more common. (But the first result for each page is actually a link to this very question in a different forum.) Salt this result liberally with the standard caveats about Google result counts being inaccurate, though.