MacOS High Sierra restarts every 10 minuts without any warning sign

Can anyone suggest what might be at fault/where to look to diagnose the actual fault?

It is nearly certain to be a hardware fault that only Apple will be able to definitively diagnose or fix. You already took all the appropriate steps to eliminate other causes.

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Determining exactly which hardware component or components are involved is not easily accomplished, but if you wish you can use the following short Terminal command to identify the numeric "shutdown code" involved:

log show --style syslog --last 96h | egrep shutdown\ cause | awk -F')' '{print substr($0,1,19), $NF}'

Copy (position your cursor in the above line and triple-click to select the entire line) and Paste that entire line into a Terminal window.

After a few moments it will return something like this:

iMac4:~ john$ log show --style syslog --last 96h | egrep shutdown\ cause | awk -F')' '{print substr($0,1,19), $NF}'

2017-12-10 07:07:15 Previous shutdown cause: 5

2017-12-10 21:11:53 Previous shutdown cause: 5

iMac4:~ john$

The meaning of those codes is not publicly documented, but some of them are commonly known. What is that numeric code?

Note: log is not present in Yosemite. If that's what remains installed you need to use another method, which I can describe if needed (summary: launch the Console app and type shutdown cause in its Filter field).