Can't tell ya about that particular CPU and setup due to what Mike mentioned -- but adding to Mikes very good points -- running even a semi-decent fan at 500-600 RPM will help everything tremendously and it won't be audible at sitting distance unless your room+system is extremely quiet. I run two multi-purpose AIO/HTPC 24/7 low-power, low-cost, miniature builds in the main room (where me better half will roast me if it's discernible over the surroundings), that were initially passive except for the PSU fan (SS S12 II 330W). However, after more than a year (and many random unforeseen problems), I've realised that for proper stability and peace of mind, and to minimize chances of component failure (particulary at the apex of summer), it's far better to run an additional fan. So we now run a 600-750 RPM CPU fan which blows out towards the back vents, past the VRMs. I never need to adjust it but even at 1000 RPM, you cannot hear it over the 2* ODDs and 2* HDDs. They - with their low frequency humming - are by far the loudest components in the system and the room.
To get it right since I would be away beyond contact, with my family depending on these builds for at least 6 months, I had to do a copious amount of rigorous testing. The builds were tested with more than a dozen MBs for finding the perfect comprises since I am not someone who will change the build every few weeks or months; I wanted it to last at least 2 years including periods where the room ambients are at 35 degrees C, and without degradation. Over fifteen 740G, 760G, 780V, 780G, 785G, 790GX MBs were tested before settling including AMD 4050e, 4450e, 2* 4850e, 5050e, 240e and 2* 235e CPUs. The main problems you'll encounter are things like poor voltage regulation (common with AMD boards), lack of fan control/undervolting options, power efficiency technologies not functioning or buggy (like PSI and C1E on many AMD boards instead of decreasing power increases it by 5-10W, or either does not do anything), overheating chipset, drives, RAM, VRMs, IDE port becoming dead every so often and/or not functioning with certain SATA combos... failing VRMs due to overheating producing an erratic/dead board, having low efficiency VRMs, etc. The greatest setback to running as fanless as possible is without a doubt chipset, VRM and HDD heat build up. It quickly becomes a furnace with one source heating the rest up. Heavily used HDDs (regular basic video load) start failing and producing errors pretty damn fast when left at higher than usual temperatures.
Other basic points to keep in mind are things like VRM/CPU power. The hotter they run, the more inefficient they become, meaning more power is drawn and more heat is henceforth output. Getting a mainboard well known for efficient VRMs is the first step as well as a MB which allows good fan and undervoltage control. GBT boards used to be the worst in terms of voltage regulation of various components and VRM efficiency, and MSI/ASRock the most superior for the past few generation of designs. I'm not sure about right now with all the new 785G and 880G designs but I know for certain that the MSI 785G E65-E51 series MBs are among the highest in VRM efficiency and low overall power. GBT low-end chipset boards are renown for very hot, crappy VRM, chipset HS, and overvolting each component above stock, specifically under load (measured - way out of design limits).
BTW, why the Brisbane 4850e?
I'm currently running a 4850e and a 235e in the aforementioned two systems. The new Regor chips are better in every department including a better ability to undervolt/overclock/set P-States/not suffer from the large CnQ performance bug. They idle at lower power and load lower. The average for my Regor 'e' designated chips was a 0.32v undervolt at stock HFM. In LFM, they all bottomed out at 0.67-0.69v (default is 1.00v). Brisbane was ~39W DC stock while the Regor was ~28W DC stock (incl. VRMs). I guess cost is something I haven't looked at as I'm fortunate to get these chips cheap from my work place contracts. This second 235e cost me something like Â£30 about 7 months back. It runs fine at upto 0.800/2.85GHz speeds, undervolted to 0.6875/1.0375v CPU, 1.05v CPU-NB, with a Phenom 9550 HSF running at the above speeds and the PSU fan stays at ~700-750 RPM. Stock volts are 1.00/1.325v, 1.175v CPU-NB. After a 2.3 hour x264 encoding load only a few days back, 32 degrees C room temperature, it broke 46 Tctl, which is the hottest I've yet seen it reach (Tctl_Max for these chip is 70).
To run the 4850e with the same setup, I had to heavily undervolt it and underclock it. Down to 2.0GHz 0.95v, and even that was pushing it in summer extremes. Hopes that helps you and others in a similar position.