Dodig/Melo are looking to become the first team to repeat as champions since Max Mirnyi and Daniel Nestor (2011-12).
Also in contention are two-time champions Bob Bryan and Mike Bryan (2003 & 2013).
Both players have been productive in 2016, leading the ATP World Tour in match wins – 42 for Djokovic and 41 for Thiem.
Djokovic cruised to a straight-set win against Tomas Berdych in the quarter-finals, while Thiem, who will enter the Emirates ATP Rankings Top 10 on Monday, saw off David Goffin after losing the first set.
The young rising star Kei Nishikori is also into the third round as well, giving Novak plenty to think about.
Despite all this stressful news, his wife Jelena is doing a great job in keeping her champion nice and relaxed.
Djokovic, who holds a 2-0 Fed Ex ATP Head2Head record against Thiem, is looking to reach his 20 Grand Slam final.