recommended temperature for CPU

Check this out on different CPUs temperature and how to get them cooler:

https://www.computerhope.com/issues/ch000687.htm

Spec, https://ark.intel.com/products/75122/Intel-Core-i7-4770-Processor-8M-Cache-up-to-3-90-GHz-
What makes up your CPU cooling, heat sink, fan?
The thermal paste might not have properly applied.

If the temperature is too high I am going to replace the cooler

Presumably it is BIOS that is making the beep and if BIOS was unhappy with the temperature it could turn the fans up so I doubt it is over-temperature. The manufacturer normally provides a utility that you can see what all the fuss is about, can't tell you what it is as do not know what motherboard you have. Could also be a RAID controller, some of them beep if the array is degraded. Presumably you know it is this computer and not something else?

I doubt it is over-temperature

I posted a snapshot of the temperature reading

The manufacturer normally provides

Is not the case with ASUS, also will it check the health of the components but if it is yet healthy it will now show a potential risk.

Could also be a RAID controller

No RAID

Do you have the heat sink, fan that came with the CPU (built your own system?)
Often issues like this relate to the thermal paste linkage to the sink. Poor heat conductor...
Check whether the asus board has a bios update that deals with the CPU you have. Potential mismatch .......

Which asus board do you have? Heat sink?

It is barely over Tcase maximum, that is the optimal temperature for energy efficiency but you really need the fan RPM as a percentage of max RPM, which you can find out from the fan spec or by making cooling worse experimentally and watching the figures.

Maximum Temp: 67°C for what? Tcase max is 72.72°C from the spec Arnold posted, and that's almost 10% different*.

Not really percent, that would only be valid if it was water, use Kelvin and 10% is more like 3%.

It may be slowing down due to poor cooling but at least it is doing it gracefully.

Sorry, not trying to be rude but the figures posted are a bit high but they are not excessively high because screenshot exists.

Not rude at all, I have no issues with someone checking my data.

All temperatures listed were for CPUs running at default (non-overclocked) speeds with stock cooler with temperatures at different usage levels:

Idle Temperature - Computer idling at Windows desktop (no open windows or programs)

Normal Temperature - Computer during heavy use (gaming, video editing, virtualization etc)

Max Temperature - Highest safe CPU temperature recommended by Intel

Most CPUs will begin to throttle (lower its clock speed to cut down heat) once they hit 95 to 105°C. If temperatures rise further, the CPU will shut itself down to avoid permanent damage.

Temps listed were that of the posted CPU on Desktop 4th Gen Intel® Core™ Processors Datasheet, Vol. 1, Intel: Core i7-4770K. That said, there are several case configurations for that processor, some of which go up to 80C, but I went with the standard version PCG 2013A as a guess. That may have been in error. So...

More detail for this processor:
Processor option and max temp for each at max wattage:
PCG 2013D and PCG 2014:  Max temp 72.72C at Max 84W power
PCG 2013C:  Max temp 71.35C at Max 65W power
PCG 2013B: Max temp 71.45C at Max 45W power
PCG 2013A: Max temp 66.35 at Max 35W power

I have uploaded the data sheet for reference.

Thanks for keeping me honest.
4th-gen-core-family-desktop-vol-1-da.pdf

Thank you for your help