Extempore means the same broad thing as extemporaneous: without a prepared script, out of the moment. It is shorter, older, and more bookish. It works two ways, which is easy to miss. As an adjective: an extempore speech. As an adverb: he spoke extempore. British and literary English keep it more than American everyday speech, which prefers extemporaneous or the plainer impromptu. Though actually, it is not a fancy extra sense — it is the same Latin phrase, just left in a tighter English shape. You will meet it in older books, exam passages, and formal notices more than in chat. The loud part of the word is TEMP.