Given that your CPU (i7-940XM) is a CPU released on Q3 of 2010 and is now discontinued, it is normal that it is suffering in terms of performance etc.

From my knowledge and experience, most CPU's have a lifetime of 5-8 years if they are taken care of decently. in this case, yours is 12 years old.

Since this is a continuous issue as you've said, you have to install versions of Kali (or any other Linux distro as a matter of fact) that is lighter and has broader support for your device. As Kali is a rolling release, the current kernel is 5.18.17 IIRC, thus I sincerely doubt that this kernel supports your CPU & hardware.

1. There was no any word about performance.
2. Have you read It is a decade old problem? There was no any version of Backtrack and Kali doesn't suffer from this problem. There is no word about any Kali supports any CPU. The linux itself is the problem. It is typical CPUs overheat under linux.
3. The problem is not the version. Doesn't matter it is lighter or not. The CPU works under all the versions of Kali.
4. According to your thinking: I would buy a new laptop year-by-year if a new version of Kali released???

As I have seen, you comment in lot of topics without any meaningful content. Just saying the not relevant generalities, nothing.
You are the typical species who must make his voice heard.
You don't understand it, don't say anything.
Thank you for the nothing.
Please don't waste others' time.

I kindly suggest you to re-read your initial comment and consider keeping your responses respectful. No one is obligated to help you, especially given your childish response. The ability to speak does not make you intelligent.

You've stated "After a fresh install during computationally intensive and non-intensive processes the CPU overheats. It happens during a simple "make -j 2" command. It happens during every process is contiuous."

This is indicative that your CPU is suffering in terms of performance, thus (perhaps) the CPU is hitting 100% usage and suffering (in performance).

Additionally, I found nothing from my searches specific to i7-940XM, regarding any performance, Linux or such issue. Please share your sources etc. that indicate this claim.

It doesn't matter if Kali itself supports the CPU. In the end, it the kernel that supports and runs your CPU. For example, as seen here: https://www.phoronix.com/news/2021-Linux-Drop-Old-CPUs

No one told you to buy a new laptop every year Kali is updated. I've been running Kali on the same Thinkpad L570 (i7-7500U CPU) for the past 4-5 years. The issue that you're not understanding here is that the Linux kernel might have dropped support for your CPU. If this is the case, you may need to use an older kernel. This might call for you to use a live-build to generate a custom ISO that uses the older kernel.

What are you talking about? It is about ARM cpus! If somebody doesn't read the link, thinks you told a relevant info now, but no.

And I say it again. It is not a performance problem. The CPU doesn't work at 100%. 25% at most! Where do you even think it works at 100%???

And before you suggest an other irrelevant generality, no, it is not a heatsink or conductor problem.

Please, don't argue semantics! Do you really want to save your status with semantics?
Searches specifically to 940XM? Yes, there is no results, specifically this very rare CPU.
Let's find "CPU" instead of "940XM"

You are not obligated to help me.
Please, don't do it!

Have you checked the thermal paste and cooling solution you are using?

If your system is constantly overheating, it really sounds like you've got something going on with your system. If this was a widespread issue, more people would be reporting their CPUs overheating.

@pure_NZ: Could you please be respectful to others trying to help you and don't insult them? Thanks

Generally i agree with the others: Probably just a hardware / device problem like too old / vanish thermal paste or dusted cooling solution or similar.

Unless the PC hits the 90-degree (Celcius) mark and cause a shutdown due to safety, the thermal paste should be "fine". Still, it isn't a bad idea to clean the old paste with some isopropyl alcohol (99%) and apply some new paste. Usually, the CPU (on laptops) will have a rectangle-like heatsink, that is connected to the fan(s), (usually located on the corners of the laptop.

Since it's a laptop, you may just need to drop a rice-grain-sized drop of thermal paste. Otherwise, a pea-size should do.

Why is it so hard to understand it is not a heatsink/paste problem? There is no any problem under windows. Contrary to it there is and was no any linux kernel can manage the temperature.
Why do you think I can't recognize a heatsink? I repair electronics every day. I am professional.

Maybe I should repeat: There is no any problem under windows. The CPU usage could be 100% all the day without any error. The linux can't do it at 25%. It was not capable to handle the temperature 5 years ago, 10 years ago, and yes, 12 years ago. It is about the linux kernels' lack of ability. Or the programmers' one.

Can you provide us with some logs? kern.log, dmesg output, something other than "it doesn't work and it overheats" because we don't do anything special with the kernel with regards to CPU usage, and if this is a decades old issue, as you claim, then the issue should have been addressed by upstream kernel devs a long time ago.

We also have absolutely no idea about. your, or anyone else's skill level or skillset, and since you've provided no additional information, and we do not have the hardware in question, we cannot reproduce or look the information up ourselves. Again, based on you saying it is decades old, I would highly recommend reporting it to upstream kernel bugzilla

This report has been filed against an old version of Kali. We will be closing this ticket due to inactivity.

Please could you see if you are able to replicate this issue with the latest version of Kali Linux (https://www.kali.org/get-kali/)?

If you are still facing the same problem, feel free to re-open the ticket. If you choose to do this, could you provide more information to the issue you are facing, and also give information about your setup?
For more information, please read: https://www.kali.org/docs/community/submitting-issues-kali-bug-tracker/