I’ll just start out by pointing out that the saying is “you have another think coming”. It’s not “another thing coming”.
The saying goes something like, “If you think (such and such), then you have another think coming.” The idiom works because it connects the two thinks.
However, because people aren’t used to seeing think used as a noun (Cambridge, Merriam-Webster, Oxford) and because the K sound in think blends with the K sound in coming, it’s easily misheard as thing instead of think.
Both versions have been around for quite a while. For example another thing coming was first seen (as far as we can tell) in an August 1919 edition of The Syracuse Herald:
If you think the life of a movie star is all sunshine and flowers you’ve got another thing coming.
However, the earliest occurrence of another think coming is at least a decade older; although it, too, was seen in Syracuse, but in The Syracuse Standard in May 1898:
Conroy lives in Troy and thinks he is a coming fighter. This gentleman has another think coming. It is probable that McCoy will next meet Joe Choynski.
One could make the argument that they’re roughly the same age, despite one being a decade older. However. one has been more popular right from the start. Far more popular.
The blue line above is for got another think coming, while, of course, the red line is for got another thing coming. Clearly, the former is far more popular, and it wasn’t even until the mid-1960s before the latter started to gain any popularity at all.
That covers print usage over the last 100 years or so. What about search queries?
Same colours.
What we notice here is that the roles have switched. People seem more likely to search for got another thing coming over got another think coming. And notice the downturn in the first graph for got another think coming. That isn’t the first downturn that phrase has encountered over the last century, but when combined with search behaviour, perhaps it’s not just a cyclical datapoint. Perhaps it’s the beginning of the end.
Those who are diehard another think coming supporters have quite a bit of support on their side, but the fight could possibly be futile in the future.