This is awkward, even with an ambient temp of 35°-40°C i haven't reached those 65° C running BF4 at max settings (maybe it's not a taxing game). I have an AMD FX-8350 4ghz, Sapphire Radeon 7870OC edition, Gigabyte 990fxa ud3 and 8gb Gskill sniper 1866 (2x4) and a viewsonic 24" full hd monitor (I'm not in my house right now and i don't remember the model). I have all that into an Aerocool templarius telum black, with one 120mm intake fan in the front, another one as exhaust in the rear, and another 3 120mm fan at the top (exhaust) which i turn on when gaming or i use them at low speed when the ambient temp is high (30° and above). The PSU (NXZT hale82 650w) is at the bottom of the case. GPU temps at idle (using firefox and watching flash contents) may rise to 38-41°. My CPU doesn't reach above 50C° (I only watched temps when I started using that computer, then i relied on the CPU fan noise, which is annoying), actually I think it's 40°C. When gaming GPU temps arise to 60-65C° depending on the title (I play league of legends most of the time, without those ugly shadows, temps doesn't reach 45°), the only time I reached those 70C° was playing metro 2033 (max settings), playing for a while, and my CPU was near those 65°.
I might add i have two old sata2 drives, but i did some cable management, which allows for a clear air flow, which in my opinion, is quite good. This is the first "high performance" computer I have built, before this one I had low-medium performance parts, and airflow wasn't so important. I'm kinda limited by the high taxes and this goverment (Argentina) but this is how far i could go. Now I'm planing on going for a new CPU Cooler because i cannot stand this stock fan, but I'm still surprised by your numbers.
Also, despite materials and building processes, Intel haswell-Ivy bridge processors shouldn't be push ahead AMD on CPU temps, because they'r built on a 22-28nm process, and the AMD parts (except GPU) are 32nm, which theoretically means they should support higher temps. AMD puts a 65C° limit just to warn you that there's something wrong and that you should consider another option just to allow your CPU to have a longer life.
PD: I do some cleaning at least once a year. I dissmantle every single part, even the coolers, and I clean every single part and I also change the thermal paste. Last time i used Artic cooling MX4, but before that i've been using a generic one (i was a bit dissapointed as I espected a little bit of difference with this change, and I only got 1°C, maybe 2°C less). I apply an special oil for fans, which isn't expensive at all (and you need one or two drops). I enjoy doing all this. You may wanna try this at least once.