Mini cutting out after a few minutes

Question

This problem has only developed in the past month or so. Basically my mini cuts out and shuts itself down entirely after only a few moments of running.
It did this once before when I was experimenting with iMovie years ago. I assumed it was the overheating safety measure kicking in as I was putting the machine under a lot of strain and the fan was going pretty loudly. As it didn't seem to have caused any major damage and it worked okay after cooling, I figured it was okay.
A couple of months ago I was running a few programs at the same time when the fan seemed to power up quite loudly again and it cut out again. Since then, the problem has become progressively worse. At first the fan would begin powering up for no real reason (running simple programs, machine temp monitor showing normal temperature) and now it will shut itself off after a minute or so of running regardless of whether I'm running any programs at all and before even the fan starts up. As such it is unusable and it is not even stable enough for me to do any real backup or get any of the important documents off the machine.
Things I've tried:
Cleared as much dust as possible from the vents that may be interfering with airflow
Made sure it's got plenty of space around it
Reset the PMU
Booted up from an external HD with a new minimal MacOSX install on it and booted up with as little connected or running as possible.
The problem has persisted.
Are there any other suggestions for things I might try? Thanks in advance.

Answer 1

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The first part of your description certainly sounds like the protective shutdown due to overheating - particularly considering the increased fan speed immediately in advance of the shutdowns. However, the second part - where you describe shutdowns happening rapidly after booting the system up, and not seemingly associated with fan activity are not quite such classically clear protective shutdowns.
Even so, it seems pretty clear your mini is suffering overheating - and the fact it has done so before, and the problem not resolved, means that thermally induced shutdown is the most likely cause of the system behaviour you describe, and that it may be that the original problem was that the CPU heatsink may not have been firmly attached or that the thermal paste may have been misapplied or quickly degraded.
In this situation I'd open up the system and make sure that any and all debris inside is removed. even after you cleared the vents, there may be a considerable amount of dust and debris that has accumulated inside the system, and given there's not much room inside the casing for air to flow, even small amounts of extraneous material in there can cause problems. While the top is off, I'd also check that the fan is actually working.
Assuming all is clear and the fan running correctly, the next most likely problem is that the CPU heatsink is loose. After that, there is a possibility that the thermal pad needs replacing. This is a small pad that fits between the underside of the logic board and the base of the system with the purpose of draining some heat away from the processor to the base, and thus away to the surface on which the system sits. In itself, a failed pad would not be expected to cause the swift shutdown of the system you are experiencing, however, so disassembling the system purely to replace this is not likely to resolve the problem directly.
I would also be inclined to look at the power brick to see if there is an issue with that. If you know someone with a Mac mini (even a later Intel model), see if you can borrow their PSU for a brief test, or better yet, take your mini to their house and test it there. If the problem continues with a different PSU in a different location, and there is no problem with the heatsink or fan, then I suspect that over time your mini has been heating to higher temperatures than normal, and that eventually this had led to heat stressing of components that has now given rise to failure. You may find that if you run the system with the top casing removed and a fan blowing on it, that it will function long enough to rescue files. Trying this would be a good test to see if the problem is directly heat related.