If you are charting and taking temperatures, once you have reached a true thermal shift you aren't going to ovulate again. Its biochemically not going to happen as the thermal shift is due to the release of progesterone from the corpus luteum in the ovary. Once progesterone is out there, ovulation is impossible as it needs an estrogen surge/ LH surge/ low progesterone environment to occur.
However, reiterating what PPs have said, it is possible, within the same 1-2 day period, to ovulate multiple times, hence twins/triplets etc. But once your progesterone spikes, all further ovulations will be suppressed until the next cycle. If you are TTA, this wouldn't concern you because you would be abstaining during this time anyway... the rules of sympto-thermal NFP take this into account.
Additionally, it is possible to have *mucus* symptoms that make it seem that you have ovulated twice in a cycle several days apart, but this is due to delayed ovulation and it isn't until the final round that actual ovulation occurs. Again, your first mucus patch could very well be when your body was intending to ovulate and it set up the environment (fertile mucus, etc) to do so... but then for whatever reason, stress, illness, etc... it decided last minute that now was not a good time for the ovulation to occur, so the ovulation was suppressed... several days later when the timing seems better, your body would then gear up to ovulate again (second patch of fertile mucus) and then would actually release the egg this time around. Oftentimes this second patch of mucus will be shorter than the first.
Therefore, women who think that they ovulate twice based on mucus symptoms alone are potentially experiencing this phenomenon of delayed ovulation.
As far as the article orginally mentioned, it basically addresses the issue of delayed ovulation... that the body can have multiple waves of ovulation preparation (luteinizing hormone surges that would register on OPKs) where everything looks like it is ready to release an egg... however, the article itself states that it is only the final wave of preparation that actually releases the egg (or two, or three) within the same 24-48 hour period.
take care
elaine