Your using evga precision right? If so, uninstall and try it again with Afterburner instead. Don't have both installed at once or youll have conflicts. if your gpu gets higher than 60c, or its supposed to, its going to ramp your fans up until it gets below that threshold. 84 is waaayyy too high to be running your gpu at, youll be lucky it lasts a year or two with temps like that all the time. You shouldn't be idling at 60c, you have multiple monitors or something too? What case do you have?

wmmills
Your using evga precision right? If so, uninstall and try it again with Afterburner instead. Don't have both installed at once or youll have conflicts. if your gpu gets higher than 60c, or its supposed to, its going to ramp your fans up until it gets below that threshold. 84 is waaayyy too high to be running your gpu at, youll be lucky it lasts a year or two with temps like that all the time. You shouldn't be idling at 60c, you have multiple monitors or something too? What case do you have?

I’ve tried with both software, neither can stop it- I have to stress that it’s a single fan doing this, and I confirmed with 2 friends who own the same GPU that that 3900 RPM is way above what their max is. 
 
I owned a 1080ti that I purchased on launch which ran at 85c all the time (thanks, Nvidia blower design). I sold it to a friend, and it’s still running. These cards are designed to run this hot thanks to GPU Boost afaik- they boost as far as they can until they hit their temperature ceiling (84 when stock, up to 89). 
 
60c isn’t idle, I opened hwinfo mid game and took the screenshot while in game. I am multi-monitor though, 1440p144 and 4k60. 

HologramParsons
I am having the same issue with my 2070, havn't had any luck fixing it, will post if I do.  Mine will turn off after about 30-40 minutes of idle computing.

Strange, I don't have the latter issue. Mine had crashed my whole computer a few times in DayZ, however in Squad/War Thunder it just spins up. It never acts up while idle for me.

Cool GTX
What software are you using to read the "Reported" fan RPM ?
 
It could just be a software error  .... running a fan above 100% would be very unlikely

Both EVGA Precision X (shown below) and HWInfo (shown above).
 

Note that it only says 81% fan speed- it doesn’t seem to be software related. I say that it’s going above 100% because 100% for my card is around 3400 RPM. 

Cool GTX
that is odd ... can you set it to a Fix RPM of 100% ?  what are the results ?
 

This is 100% speeds: 


 
I'm 99% sure it's not a Precision issue, I only installed Precision X1 again to see if there was a firmware update available. 

Gatortribe
Update: It seems to do it every time it hits 82, which is pretty much always unless I want to run the fans at 100% with an aggressive curve or reduce the maximum power of the card.

I know it's an old post but did you find a solution ?
I have the same problem as you and since a few days my RTX 2080 Ti Black has spikes at 3900+ RPM on the first fan.
I tried to change the curves but that didn't do anything and the fan keeps going crazy randomly.

Yeah that happens when it hits 83°c.
I've had that card for more than a year and it never happened before.
I can see in Precision X1 that in the Temp Tuner tab, if the card hits 84°C the frequency is drastically reduced, is it to avoid that ?

I have the same issue with my RTX 2080 XC ultra. SInce about a week, once the temp. reaches 75c the fans go from 2000rpm to 3200 and its very loud.