On the PSU side: What is your PSU's 80+ rating (you only mentioned it's 80+ so then it could be White)? It should be at least Bronze if you run above 600w. I'd go for Gold 550w over White 600w any day of the week. I doubt your config even needs more than your 700w (TBH, I think a 600w may be fine), since your video card is the only big draw and on 30% load, it will probably draw under 100w. That 80+ will may well determine if it's handling the demand.
Source: see my specs below (except GPU OC'd a little by the OEM), 8 fans total, and I actually have 2x 3.5" 6TB HDDs (one is purely a backup). I'm on a 550w 80+ White and I'm fine with my PSU, even when encoding video/rendering 3D. The major difference between our rigs is your video card, which is only hitting 30% load (about 70w), putting it around my card's power anyway. You have an extra 150w compared to me.
On the CPU side: How long does that temperature (65-75 C) remain? I'd stress test it for an hour (during which time you can see if it reboots). Try running Passmark's Memtest, too. Just in case it's memory-related (could be on-chip controller for example, not necessarily dies).
It could be down to other thermals, too, like your PSU's. Check everything coz the CPU can be kept cool at the expense of Memory temps for example. Airflow that pushes past components can cause dust to settle on things that usually don't need fans because dust will trap heat between the fins of heatspreaders etc. Dust is an enemy of rigs like ours that have lots of fans/airflow. A can of compressed air does wonders.