“Then” is an adverb and cannot be used as a conjunction, even though many of my students think it can.
Wrong: I went swimming, then I took a shower.
Right: I went swimming, and then I took a shower.
One way to show that “then” is not a conjunction is to move it around in the sentence. “I went swimming, I took a shower then.” “I went swimming, I then took a shower.” You can see that these would-be compound sentences are actually run-ons even with the word “then” in the sentence. They need a coordinating conjunction such as “and” or a subordinate conjunction such as “before.”
Many students use “then” as the first word of a sentence to show a time sequence or a transition from one idea to the next. Students might need to do this as they write down events in chronological order. But often they overuse the word “then,” with some students starting almost every sentence with that word. An easy way to deal with this problem is to let the student write “then” all she wants in her first draft. During revision, have her circle every “then” and cross out all but one. Let her choose which one stays.
Some grammar books indicate that “then” should be followed by a comma when it starts a sentence, or when it interrupts a thought. A comma indicates a pause in thinking or in speaking, and since we Americans don’t usually pause after the word “then,” it is rarely necessary.
“Then” is one of many overused words by students, along with “so,” “just,” “like” and “and.” Usually when students are made aware that they are overusing a word, they self-edit, but sometimes it takes several revisions to prove that they overuse certain words.
Also, “then” and “than” are not synonyms. “Then,” like “when,” indicated time. “Than” indicated comparisons.
English Writing Teacher 
Moving the word “then” to the end of the sentence doesn’t work, but it doesn’t prove the word can’t be used as a conjunction. It would similarly not work if you moved ANY conjunction to the end. Try this: “I went swimming, and I took a shower”, Now, try: “I went swimming, I took a shower and.”
In my opinion, the (academic world’s) insistence that the word “then” can’t be a conjunction is precisely what made the word “redundant” or “overused.”
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I believe we should be more flexible in this case and allow the word “then” to be used as a conjunction. The academic world’s insistence that “then” is not a conjunction is exactly what has made it the “overused” word that it is.
It’s true, as you pointed out, that moving it to the end of a sentence wouldn’t work, but it would similarly not work if you move ANY conjunction to the end of the sentence that it’s supposed to “conjunct” with the previous one. Try this: “I went swimming, and I took a shower.” And now this: “I went swimming, I took a shower and.”
My suggestion is: in all cases where “then” means “and next”, the word should be allowed as a conjunction, simply by virtue of its very MEANING. Grammar is nothing but a tool to let us correctly interpret written communication. I can’t see any situation where my suggestion above would make interpretation difficult or potentially erroneous.
Likewise, I suggest that a few other words are also candidates for such treatment—“even”, “perhaps”, “almost”, “indeed”—under appropriate conditions. You so need to precede it with a comma.
Example sentences:
1. “A compass is highly recommended, EVEN indispensable, on this hike.”
2. Same sentence, but replace “EVEN” with “PERHAPS”, “PERHAPS EVEN”, “ALMOST”, “INDEED”…)
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