First check if your CPU is overheating. According to your description, it is possible that your watercooler is not functioning properly. As far as I know, an overheating CPU usually triggers a shutdown instead of a sudden "power-cut" to the computer as you have described in your linked question. But the watercooler having a great temperature difference like you have mentioned may be a problem. And if the computer shutdown is triggered by an overheating CPU, it may take some time for the CPU temperature to go below the threshold value which can make it take some time before you can boot it up like you have said. For you to be sure that it is not a problem with overheating, it's better to check it and cross it off the list.
What I would suggest is that you install a hardware monitor (HWMonitor by CPUID is a popular choice), or enter BIOS and monitor the CPU temperature.
If your PC shuts down when temperatures reach around 90°C+ (or the threshold specified in BIOS which some motherboards let you specify), then it's time to inspect the CPU cooler. Check whether the CPU cooler is mounted properly and that an adequate amount of thermal paste has been applied. If those are OK, remove the CPU cooler and check that. If it's a sealed unit which you cannot disassemble, try and check if you can hear or feel the water being pumped through the tubes. A faulty water pump can make the water block quite warm and radiator cold as you have stated. If none of them are at fault, then it's not a problem with the CPU overheating.
The second major component that I suspect is the PSU. Connect only the essential components of the Computer and boot it up. If the computer doesn't power down, connect the other devices one by one until it powers down. Then connect that last device which triggered the power down to a different cable from the PSU to identify if a particular connection from the PSU is at fault. Also try connecting a different device to that connection from the PSU to check if the device you connected is faulty. If you have a spare PSU, swap the PSUs and check if the computer powers down.
I saw that someone had suggested in your linked question that you change the RAM modules and check. How did that go?
Finally, can you tell us if your system is overclocked? If you have, bring the system back to its stock settings and check. An unstable overclock can result in the computer powering down.
When trying to diagnose a problem like this you may have to check different component and connection combinations. (ex. HDD with SATA power connector 1 or HDD with SATA power connector 2, RAM module in slot A, etc.) so that you can eliminate the suspects one by one. You may have to let each combination work for some time to make sure that it is not the faulty part.