Here's my vote : the "think" version is original and logical and the only version I have ever consciously heard. However, it appears that owing to dialect pronunciations it has sometimes been heard as "thing" and repeated so that this version has become in some places or social milieux too established to be called "wrong". But among well-educated native speakers of standard British English (what the BBC used until a few years ago) it is still wrong.
The proof that "think" is the original version is found in the fact that the expression is never used unless the word "think" has already occurred earlier in the sentence ("If you think that...") No synonym will do.
BTW Google hits :
"You've got another think coming" = 325000
"You've got another thing coming" = 41200
"You've got another thing coming" -Judas = 24800
The thinks have it !