The example sentence has a rather complicated subject so I will try to simplify my explanation for you. ACTIVE voice: subject = he; verb = remembered; object= the dragons said to be guarding vaults in the wizards’ bank. To make the sentence PASSIVE, the object (the dragons...) does the action. With an unpleasant jolt of the heart, the dragons said to be guarding vaults in the wizards’ bank were remembered. I agree with Dan Smith. It's not a great sentence in the passive voice.

Your reconstruction is not in the passive voice. The core of the sentence is "he remembered the dragons." "He" is the subject, "remember" is the verb, "dragons" is the direct object. In order to turn it into the passive voice, the subject has to go away, grammatically: "Dragons were remembered." We can sneak the subject back in as an indirect object, "Dragons were remembered by him." Your sentence is very difficult to put into the passive voice because it has so much in it about the subject, "he." We could say "Dragons were remembered as guarding vaults in the wizard's bank" or "With a jolting of his heart, dragons were remembered by him as guarding vaults in the wizard's bank." I believe these are correct grammatically and in the passive voice. (As a matter of style and good writing, they are very ugly, though!)