Hi,

You can fix it with HPFancontrol:
http://tpfancontrol.com/
I have HP 1040 G2 with same problem. Fixed with HPFancontrol. You can tune rpm very smart. Recommended.

I've been using this laptop for a month now and confirm the reported problem of oscillating fan. The G3 1040 activates the fan at CPU usage even around 10% (room temperature of ~23 deg. C) and making annoying speed oscillations! They are not noisy, but very annoying in quiet environments. In this regard shame on HP in my opinion. Otherwise, this is a great laptop. 

Just my short view on this machine and its downsides (HP in general have proven to be ok).

I searched for a long time to find the ultimate laptop and ended up in the higher price range due to my specific requirements of a matte QHD screen.

Unfortunately I had issues with coil whining and oscillating fans in a quite room which made me practically go insane - so I returned it hoping it was a dud. But to my disappointment I was stuck with a (on the paper) perfect machine with major manufacting design issues and returned it once again - this time opting for a full refund. Luckily HP was very responsive and accommodating during the whole process so I will give HP a new chance in the future but not on this machine.

Do not recommend the Elitebook 1040 G3  if you are sensitive to noise and often work in a quite environment.

Regards, Christian