DON'T RUN KILLER DONUT EVER AGAIN. FURMARK IS NOT GOD TESTED. IF YOU WANT MAX YOU COULD USE FURMARK BENCHMARK NOT STRESS TEST.
For any temperature test you should open side panel install card and start Firestrike, 3DMark 11, Unigine Heaven or even better games... Fan on 70-80% manual and open side panel. Than you will know real temperatures of your card. Manufacturers of graphic card can't do nothing to graphic card so powerfull and naturally hot stay cool in closed case, nothing. Simply such cards need very big case, at least 4-5-6 very good 120mm fans only for single card to cooldown. Imagine how fast spin 2 fans from graphic card, 2000-2500RPM, they blow 80C constantly, how much 120mm fans need to work on 1500RPM to compensate that... Many of them, it's not even possible. Every temperature result you look on net are tested in these conditions...
You can install same, set manual on 70-80% and check temps, I can bet results will be 15C or more lower temps. Off course some things could help you lot, as Vsync... I don't know how that work with AMD, but with NVIDIA very good, and why card to work on 99% even in games where reach max fps on 60% usage... that's 10C less... And if she can't provide enough fps than she will work on 99% anyway. If your monitor is limit on 60fps why to leave card to give you 150 constantly...
Today with high end graphic card and overclocked graphic card, I mean cards with over 240-250W power consumption only way is to customer tolerate little noise and open side panel or to install watercooling. Sometimes help only to little open panel, not completely. Because of that case with some kind of door or lock are welcomed. 650D, 600T, 760T, Caselabs, some Thermaltake and Lian-Li case...and others... If not cards with 180-190W power consumption as GTX980 work on lower temps. That's it. Many people today buy R9-290 or R9-390 only to invest rest of money in waterblock, overclock card and get something similar as R9-290X and R9-390X.
Fan on Auto? You can keep fan on Auto with some reference card if they blow air out of case, with some aggressive fan profile. Dual fan graphic cards with non reference PCB should be keep with very aggressive fan profile or manual on 80% with possibility to hot air have open space.
Why you don't want to disable all case fans and open side panel and set fan profile on graphic card at least 70% and than run Firestrike. 78-80C would be normal temperatures. You will see better temperatures without single case fan if side panel is opened than with 4-5 fan in closed case.
Wait, you will leave Matrix Radeon graphic with finest build...:) It's true ASUS best models are GeForce, but that's because 70% of customers search for GeForce and ready to pay premium. I can bet your graphic card could work on safe 80C with 80% fan speed with side panel little opened. Same will be with Lightening and Sapphire. R9-290X and R9-390X and Fury X are card for watercooling on first place. If you want lower temperature, same memory size, same performance you should chose GTX980. And I love cards with 250W power consumption, high end but overheating is when you can't drop temperature from 95C no matter you do. And I hear that ASUS use cooler from GeForce for R9-290X but because they are launched first and from that picture I see cooler enough to cooldown graphic processor.
If you temperature really continue to grow over 85C with fan on 80% and open case you need to send message to technical support and RMA card. I know it's noisy but if cooler cooldown card you need to tolerate noise on 70-80%. Your Temperature in Firestrike should not pass 80C with 80% fan speed and open case. If temps go above that's overheating... What other people say? I hear for complains and customers talk about GTX cooler on Radeon Matrix but I thought that's not massive problem. Best call your ASUS distributor and ask RMA, if they no same card it would be smart to pay extra money for ASUS R9-390X Strix. She have triple cooler and better cooling and 8GB video memory. Forget on MSI, GIGABYTE,... Sapphire... situation could be similar only inferior PCB and components and VRM and look. I see now ASUS have two R9-290X Matrix, Platinum and normal. You say your is normal, what is difference between them. Clock?... What they change else? Pipes are different, or VRM, memory, or only clock? Even if you pay 150-160$ more you will be in better position, but maybe they will replace you for Matrix Platinum. But situation will not be some big difference. You will need to tolerate little noise and card to work on 80-85C... But she will not go on 90C and you don't need to keep fan on full speed. Max 80% maybe even 70%.