Would a right-wing third-party candidate do well in all Republican states?

[FerrisBueller86]

There is speculation that the nomination of a liberal or moderate Republican would lead to a third-party run by a real right-winger.  It's a given that such a candidate would do well in Utah and in the Deep South.  Would this third-party right winger do well in all Republican strongholds?  How would such a candidate do in Idaho, Montana, Wyoming, Colorado, Arizona, North Dakota, South Dakota, Kansas, Oklahoma, Kentucky, and Indiana? 

On the one hand, some of you think a right wing third party candidate would do well in these states.  On the other hand, some of you think these states are so devoted to the Republican name that even a liberal Republican (like Senator Snowe or poster WalterMitty) would win these states against even a conservative populist Democrat.