First of all, I would not recommend that you run the system with the fan turned off. Remember that there is only the one fan in the system and that it is responsible for the cooling of *all* of the components making up the system. It is possible to get into situations where the processor is not heavily utilized - and thus doesn't get to the temperature range where the fan is turned on - yet other components are working and getting hot yet don't have any airflow to cool them. The result is component failure.
PWM-controlled fans are spec'ed to operate above some specific duty cycle. Below this level, their operation is dependent upon fan type. There are three modes of operation defined in the PWM-controlled fan specification, In the first mode, the fan will run at full speed. In the second mode, the fan will continue to run at some minimum speed. Finally, in the third mode, the result is undefined (for example, once duty cycle falls below the minimum, the fan shuts off or it runs unreliably).
I haven't looked at the fans on the latest series of NUCs, but, in previous testing (through the Haswell generation), the minimum duty cycle for the fans in use was in the neighborhood of 25%. I would recommend that you use this as your minimum duty cycle.
Try this and let me know if the spiking goes away...