You say that the GPU Temp maxed out at 72° and that should be OK, but it might be card specific. I had a Quadro 4000 on a Lenovo workstation that would cause instant shut down when it hit about 90°c, even for an instant. The code is built in to immediately power off the computer to prevent damage to components. Run HW Monitor (https://www.cpuid.com/softwares/hwmonitor.html) during your day and it'll note the peak temps. My problem: DUST. My machine was  in an open rack but near the floor and I'd neglected to clean it out. It was massively overheating, but a good clean and all was well. However some cards are much worse than others and to be safe I swapped the Quadro 4000 for a K4000 which uses less power and stays much cooler. 

If it's not heat (and the inbuilt "protective shutdown") it could still be that one spot of GPU memory that's duff or any number of things. PSU's are often the culprit for bad behaviour - they don't last forever and fluctuating power causes all sorts of symptoms, like disks dying (so you think it's just disk failures) and so on. Again, HW Monitor will show you voltages....good luck, there's nothing worse than trying to narrow down nasty problems like this. It's worth collecting a box full of spares so you can try replacing one bit at a time to narrow things down. Also, get a replacement PSU to keep in storage - they won't be available forever for some of these custom-design machine

I'm only talking about dust and muck building up on the fans and vents to restrict airflow, so if your fans are all working and there's no obvious clogging you should be OK (again, monitor the GPU temp to see how it's going). I'd be borrowing another graphics board to try out if possible - although blown graphics boards are not a good thing it's much better to be able to pinpoint the problem to a single replaceable card. I did have a Quadro go belly-up after only a year or two (it was replace under warranty) so a faulty card can happen, and is one of the least nasty outcomes. A bad PSU always leaves you wondering what else might have been damaged...

Is it turned out yet what was the problem? I have got the same issue... Thanks.

I have the exact same problem with almost the same components. It's honestly driving me mad.

These are my specs:
CPU: Intel Xeon E5-1650 v2 @3.50GHz
GPU: Nvidia GeForce GTX 1070 Founder's Edition 
RAM: 64Gbs DDR3
OS: Win 10 x64
Storage: (1x) SSD Sata III 2.5" (1x) HDD
PSU: 685W Stock

This is what I've tried so far:
I replaced the CMOS Battery.
Tried running the PC with another GPU (GTX 1080)
Installed Win 10 on both SSD and HDD and ran them separately
Tried 2 different Monitors (I thought it was a monitor problem)

Nothing helps and like you said @AcesOfSpade it keeps freezing randomly with the only remedy is having to perform a hard shutdown. Have you solved the issue perhaps?

@Krokodilus @Zzeino  - The issue ended up being a bad video card, I probably should have gone with a more refutable seller from ebay. After I replaced my card with an RX580 8GB I had no issues.

I replaced my GTX 1070 8gb with my friend's GTX 1080 8gb (that had no problems for him) and the same issue still persisted.

I can't think of anything else to do but replace the whole motherboard, which is gonna force me to replace the RAM (since they're DDR3) and the CPU. 

I had my motherboard changed by Dell Support but still problem persists. Also tried diferent graphics card. Also no heat anomalies. Other ideas?

@AcesOfSpade  Sorry to bother, but I see you've put in an RX580, I'm planning to do the same, but the power requirements of that card is stressing me out. (Sapphire Nitro+ RX580 8GB ~ 235Watts).

May I ask how you set it up power connection wise? (my card needs both 8 pin and 6 pin)

How much power does your card draw?

(I made a post about it here if you want more info) 

same problem with 3 different pc