No — "but" is lowercase in the middle of a title in most style guides.
"But" is a coordinating conjunction and stays lowercase in the middle of a title in AP Style, Chicago Style, MLA Style, NYT Style, and AMA Style. It is capitalized only in Billboard Style or in the first or last position.
The word "but" can also function as a preposition or adverb in certain grammatical contexts. However, for title capitalization purposes, it is almost always treated as a conjunction and lowercased accordingly.
Note that "but" at the start of a sentence or title is always capitalized, as the first-word rule applies universally. Some writers begin titles with "But" for rhetorical effect, and the capital is correct in that position.
In Billboard Style, "but" is capitalized along with every other word. This style is common in music and entertainment where every word in a title appears with maximum visual weight.
"But" functions as a coordinating conjunction that introduces contrast, and all major style guides treat it the same as other coordinating conjunctions. It is lowercase in the middle of a title in AP Style, Chicago Style, MLA Style, NYT Style, and AMA Style.