Hi Andrew. I received my Part 107 Rating and temporary certificate on 9/26/2016, and I have yet to receive my permanent card, but it should be any day now. It looks like there is about a 60 day wait which is well within the 120 days that your temporary certificate is good for.
I am basing this on the FAA Airmen Certification site where they post the date range of temporary certificates that they are currently processing. You can find this site here:
Airmen Certification. The date posting is in the 'News and Highlights' box toward the top of the page.
As a note however, I noticed when I checked this just now, that a date is not showing, but this has to be just a temporary anomaly. I checked a couple of days ago, and it said 09/10/2016, so it's nearing my date of 09/26/2016.
Over the years, I have had a lot of FAA temporary certificates, as I'm an A&P mechanic, flight instructor, and ATP rated pilot with type ratings. I suggest laminating your temporary certificate, as two months is not an uncommon wait time to get your permanent card.
Hope it helps and Happy Flying!