I'm getting the same Processor Thermal Trip message as well. I've only had my NUC two days and I get the thermal trip warning roughly every other boot. My system at the moment is:
Openelec 4.1.2 from USB stick.
Crucial 4GB so-dimm
No internal disk drive (yet)
I suppose my question is; does it matter? It's annoying, but does it mean there is any damage being done? It runs perfectly well once booted (Openelec reports operating temp of about 44 degrees Celsius). I bought it through amazon.co.uk, so should I contact them for a warranty replacement? Is it likely that the replacement will also have the same issue? Is this a design fault inherent with NUCs?