The Collaborative International Dictionary of English v.0.48:

Extemporize \Ex*tem"po*rize\, v. i. [imp. & p. p.
   Extemporized; p. pr. & vb. n. Extemporizing.]
   To speak extempore; especially, to discourse without special
   preparation; to make an offhand address.
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Extemporize \Ex*tem"po*rize\, v. t.
   To do, make, or utter extempore or off-hand; to prepare in
   great haste, under urgent necessity, or with scanty or
   unsuitable materials; as, to extemporize a dinner, a costume,
   etc.
   [1913 Webster]

         Themistocles . . . was of all men the best able to
         extemporize the right thing to be done.  --Jowett
                                                  (Thucyd. ).
   [1913 Webster]

         Pitt, of whom it was said that he could extemporize a
         Queen's speech                           --Lord
                                                  Campbell.
   [1913 Webster]

WordNet (r) 3.0 (2006):

extemporize
    v 1: manage in a makeshift way; do with whatever is at hand;
         "after the hurricane destroyed our house, we had to
         improvise for weeks" [syn: improvise, extemporize]
    2: perform without preparation; "he extemporized a speech at the
       wedding" [syn: improvise, improvize, ad-lib,
       extemporize, extemporise]

Moby Thesaurus II by Grady Ward, 1.0:

28 Moby Thesaurus words for "extemporize":
   ad-lib, be caught napping, be surprised, be taken unawares,
   be unprepared, cook up, dash off, do offhand, fake,
   go off half-cocked, have no plan, improvisate, improvise, jury-rig,
   knock off, lash up, make up, play by ear, scrap the plan,
   strike off, throw off, throw together, toss off, toss out, vamp,
   whip up, whomp up, wing it