Sorry Pooh, according to Webster's dictonary, a conjunction is: "an uninfected linguistic form that joins together sentences, clauses, phrases or words."
It is thus perfectly proper to begin a sentence with a conjunction--assuming that stylistically one wishes to join ideas together. Or, as with "but," one may wish to make a distinction from the preceeding sentence.
Thus, one may wish to express one idea in a simple sentence. And one may wish to amplify it with a further exploration in one or more sentences. But one may also wish to point out an important distinction later in the paragraph!
Paragraph one: I agree with.
Paragraph two: I personally don't start sentences with conjunctions, but as I stated in my first post, some people do, so who am I to stop them? I said it wasn't a rule but more of a guideline.
Paragraph three: I would have written that as one sentence, but that's just how I write.
"It was hot. And it was windy. But it wasn't humid."
I don't think the above is well written, but you might think it is. Each to their own tastes