Hardware has been running well for three years. It has been perhaps three months since I last
booted. In last three days I've gotten a beep at different random times, perhaps 1-2 times a
day. Nothing is reported in the logs. Xsensors report CPU at 127 C. Fans and temperatures seem
normal, but it has been some years since I worried about these things.

What is a troubleshooting procedure for random single occasional beeps? Wouldn't any beep be
reported in a log?

Not if it comes from the BIOS. Those are pretty high temps - check your BIOS alarm points. I recently had to adjust mine on an old quad core I've had for years.

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I had that! Turns out I had to replace the battery in the smoke detector I've installed on the ceiling in my computer room (OK, it's a cupboard)

Play Bonny!

Syg00, your suggestion that BIOS alarm thresholds might be a bit low didn't occur to me and should have. Thanks for the prompt. Backups here are automatic.

I gather that max quad core temperature is 88 C. and they should normally run under 80 C. My Haswell i7-4790K Quad-Core was bought in September 2014, which I don't think of as particularly old.
It is not overclocked. Is there any reason to believe CPUs run hotter in time, perhaps because of thermal paste deterioration? I suspect I may have accumulated a lot of dust that needs to be cleaned
from air filters, etc. I haven't opened the box for a year or two. If that does not bring the temperature down, I may have to replace the CPU thermal paste. If my CPU is running 127 C. and 88 C
is the max for this CPU, there is an obvious need for an immediate fix, and I'd hesitate to just adjust BIOS thresholds.

Hi,

Regular maintenance on the hardware would help. Clean out the box and vents. Dust bunnies are not cute but can cause you problems.

You may need to replace the heat sink compound. Be sure to remove all the old compound and use a reputable compound like 'Arctic silver heat sink paste'. I have used it for years with no problems. In the past I would sometimes routinely replace the compound after a couple of years. Even 'Artic silver' will solidify if the temps change dramatically over prolonged periods. Most of my hardware is run 24/7 with regular maintenance performed via spiral bound notebook system logs that I maintain for each. Good idea to use system logs to make entries for any changes or problems with solution to help trail a problem.

Hope this helps.
Have fun & enjoy!