Uh-Uh, This isn't smart advice to say temps aren't an issue to be concerned about.
CPUs have defined thermal ratings for a reason.
Read the specs for your chip at CPU World under "FX-Series", this info is found around the middle of the CPU model's page taken from AMD's specs on the chip.
http://www.cpu-world.com/
Doesn't matter if it won't outright kill the chip it's not good for it and promotes degredation. FX chips will operate at higher temps but to take things to the limit isn't suggested at all, if you can do something to reduce temps from where they are now I'd do it.
Stability starts going out the window with many FX chips at or above 62C while others may tolerate more heat. Even temps around 55C can contribute to problems with stability at times depending on the chip in question.
Yes, 100C WILL damage it if steps aren't taken to reduce temps when you see this - The damage may not be apparent at first but it won't take very long for it's effects to begin showing - Even temps at 80C aren't good for it for too long.
Just because it can go that high period does not mean you should let it, while it may survive for a bit with these temps it certainly isn't good for the chip itself.
To say temps are a non-issue is bad advice and also contributes to misinformation on the subject.
Read the specs for the chip and try to get things within spec or as close as you can get it.
EDIT: A good aircooler if you have to run air would be the Scythe Grand Cross, it's a larger cooler with plenty of cooling capacity. Finding one isn't too hard, in fact many of the Scythe coolers do just fine with others such as the Cooler Master Hyper 212 EVO being a cheap yet good unit to run. Note that both coolers named are fairly large so space within an enclosure should also be considered before makiing a choice here.
Personally I'd go with the Scythe between the two if possible but in reality you'll do best running water for cooling it. A rad that's at least a three fan unit/triple rad would be what I'd suggest for the 8370, kits that use this rad would be what to look for, ones with 4 fans/quad units would do better - Only problem would be in just getting one.