Sorry for my ignorance, but does the BIOS do such a bad job? (I assumed both SpeedFan and BIOS would adjust fan speed in response to temperature, and that SpeedFan's main advantage was that I could adjust the rate at which this happened. I thought the only problem with using the BIOS was that it would be too aggressive in ramping up fan speed.)
Another advantage of using SpeedFan is that you have three thresholds: a first one for the minimum speed, the second one, higher, at which you may use an under 100% speed, and the last one (the safety control) over that the fan would run at 100%.
Moreover you may adjust any single fan speed with reference to more than just one sensor (while BIOS cannot do it: so you could ramp up the fan if CPU temp exceeds one threshold, but also if case temp exceeds its own thresholds, with SpeedFan).
And this is my optimal scenario.
But I was referring to the fan when speaking about checking in time: with ageing usually the fans lean towards starting/running differently, I mean at different voltage than when brand new.
So, with such semi-passive cooling, IT MIGHT BE POSSIBLE that after a year or two, using the BIOS, your fan may start at an HIGHER voltage (thus at an higher temp).
And therefore I've just recommended to do not fire and forget your setup.
With all fans locked on maximum, the core temperature runs from 0-40C depending on load.
As you may note, a core temp CANNOT be under the ambient level: my 45W AMD Athlon II X4 CPUs cannot run under 30° C with an ambient of about 22° C.
I think you have to investigate that using different tools: HWInfo32, HW Monitor or Open Hardware Monitor, Real Temp (if it works with your AMD), TMonitor, SpeedFan, a trial AIDA64 and so on, looking for some more consistent readings.
Even the BIOS internal readings may prove useful (just for example, if you found a stable CPU temp > ambient at idle with it, when the fan doesn't spin, then you'd find your "gap", the one needed to calibrate the other software readings).
Or you may use some Linux live distros (hoping they may give different tools/readings).
Assuming these temperatures correct for Tcase, though, that upper limit of 40C is actually at least 60C (given a room temp of 20C) and hence Temp3 is 70C, or about the maximum you mention. Does your figure also correct for case temp, or is it an absolute number? (Have I under-dimensioned my cooling?)
Personally I don't think that a Xigmatek DTH cannot cool properly a (basically) 2.9GHz Athlon II, even if running in that semi-passive way.
Nor it looks like you have under-dimensioned anything, at first sight.
So it would be still a matter of incorrect readings, if in case.
But I have no way to test those readings, so I can't help more about them, sorry.