Another think coming is the original form of the colloquial phrase aimed at someone who has a mistaken view. It comes from the old comical expression, If that’s what you think, you’ve got another think coming.
Because think in the second part of the expression is (intentionally) ungrammatical, some people hear another thing coming and repeat it as such. Plus, another thing coming usually makes literal sense, so it’s now more common than another think coming.
The exact origins of another think coming are mysterious, but it appears to be an Americanism, and it does predate another thing coming in the sense expressing disagreement. It goes back at least a century. Here are a few old examples:
Having elected him republicans think they have some voice in the distribution of the spoils and there is where they have another think coming to them. [The Daily Argus (1897)]
Those who thought taxes high in the past will have another think coming in the future. [Clinton Mirror (1907)]
If this Good Will Campaign is not a close race then you have another think coming. [Steuben Farmers' Advocate (1925)]
The original phrase still appears occasionally—for example:
[A]nd if you think I’m spending too much time on this, you have another think coming. [Washington Post]
If you think Southern women are such dainty little things, so fragile and delicate, you’ve got another think coming. [Daily News Journal (article now offline)]
But another thing coming is now more common than the original. These examples were easier to find than the above ones:
Conservatives have another thing coming if they think they can improve their fortunes by changing the subject to the non-Medicare parts of their budget plan. [Center for American Progress]
If you think you can move to an isolated cabin on a high mountain for 30 years, validate yourself and come back “whole,” I’d say you had another thing coming. [Las Vegas Review-Journal]