CC class here requires a total of 47 rounds expended in about 10 - 20 minutes, with varying numbers of rounds fired at 3, 5, 7 and 10 yards. I did not use my Taurus 851 (a close relative of the 85) for the class.....but I do use the 851 as my primary CC gun....and I shoot it often for practice. I shoot strings of 5 rounds (1 full cylinder)....loaded and fired at a rate that I will go through about 50 rounds in 20 minutes or less (with no deliberate cool-down time in between). I have never had a heat-related decrease in accuracy. That is, the gun will shoot groups just as tight at the end of the roughly 20 minute session as it will at the beginning. My 851 is an all-steel gun, so I can't speak specifically about the alloy-framed 85s.....but I can guarantee that a 12 round string for your CC class will NOT be a problem. I seriously doubt that 40 rounds in a fairly short period of time will be a problem, either.
The solution for any concerns about the shooting practicum for the CC class is to PRACTICE repeatedly at the required distances, with the gun and ammo that will be used for the class....and with the target type that will be used. If 15 yards is required for the class, then concentrate most of your practice at THAT distance. You could even do ALL of your practice at 15 yards. If you get comfortable at 15 yards, I promise that 3 and 9 yards will then be EASY.
I have been shooting handguns for about a year....and I never practice at less than 10 yards. On the CC class shooting test, I shot 100 % (47 /47 in the 10 ring). I attribute that to being very comfortable at 10 yards and a bit longer - so the majority of the 47 rounds expended, being fired at 3 or 7 yards...came very easy for me.
Finally, a word of praise to you about your planning and practicing for the class. Bravo - you are to be commended on that.
You would not believe the number of participants in MY CC class who either were not comfortable shooting the gun they used for the class....or did NOT know how to operate that particular gun (having never fired it before !).....or, in ONE case, which I still find incredible....the individual brought a 1911 pistol (45 ACP) - with 40 S&W ammo !!! He fired ONE round, then the gun jammed....and the instructor cleared it and discovered the problem. That, after just before (during the classroom session), the instructors covering IN DETAIL why it is SO important to KNOW one's firearm and be comfortable with it - before even considering using that weapon for SD !