Well, I just ran a virtual Daytona 500 at iRacing.com, 3hrs and 39minutes my card was at load and the temps peaked at 88c with the fan on 37%. Maybe laving it at auto and letting it do its thing is the best bet. Who knows.
Looking at your case.. a total of 7 fan slots, all except that small one behind the mobo wall are 120mm? How many and where are fans installed?
Your card should be running cooler. Mine in an Antec 1200 (lots of airflow) ran much cooler. If you're only running the couple fans that shipped with the case, it may not be enough. That front fan is only 1200rpm, it's quiet but not doing much. A single 120mm on the back wall is helping but if it's a low rpm fan too.. And IMO, that small fan behind the mobo wall is useless. If it came with one and it's noisy, I'd rip it outta there.
Try gaming with 40% fan speed and side panel off. Check temps. If they're lower, suspect case heat buildup. If you're already running with 120mm fans in the side panel and on top, then I'm wrong. If you're not and running with side panel off brings temps down, then I'm going to recommend additional cooling.
And I must, for those who need it, add a disclaimer: It's noted that the 5870 is designed to operate at mentioned temperatures.