The CPU core temperature is over 110 °C. Is it too high?

Are these temperature values below the permissible level?

The max temperature for many CPUs is listed in the 105-110°C range. But for long-term use, you’re much better off keeping things below 80°C in general and only pushing up to 85°C at the most

To make sure your software is giving you an accurate reading you could compare the results with those of another temperature monitoring application. There are several free lightweight tools to monitor your CPU temperature, one of which is Core Temp.

It would be advisable to check your heat sink to see if it has been dislodged, or that the thermal paste is still connecting the heat sink to the CPU, as running your CPU at that temp is sure to cause damage in the long run.

The GPU temperatures that are shown in your question are not in the danger zone.

You're well into the range that can cause permanent damage to the CPU. Most consumer electronics (including CPUs) are not designed to operate above 85 °C for any extended period of time, and most will actually shut down when they get over about 100-105 °C. Provided you have a working (and properly sized) cooling system and are not somewhere with unusually high temperatures to begin with (40 °C or higher), you should not be seeing temperatures that high no matter how hard you push the CPU.

However, I'm inclined to believe something is wrong with your system due to that insane discrepancy between reported package and core temperatures. In particular, the possibilities that come to mind are:

• The sensor isn't being read correctly and the core temperature is actually much lower. This is the best possible case, and it's easy to check (try a handful of other tools for reading these sensors. Everything else reporting similar temperatures does not rule this out though, because the drivers being used to make the reading may be bad (you can check that case by booting into a live Linux environment and seeing what it says the temperatures are. I know 100% for certain that Linux reports the temperature correctly on that model of CPU because the sensor interface the CPU provides has been around since the AMD K10 days and is very well supported by Linux).
• The sensor isn't being read correctly, and the package temperature is actually much higher. This is extremely unlikely, because for it to be the case you have to have somehow managed to run a CPU with a 20 W TDP so hard that it got that hot. The only possibilities I can think of that would allow for that are running with no cooling system at all or running in an environment that was already unlivably hot for humans.
• Something is wrong with one of the temperature sensors. It is not very likely, but it is still possible. If you've eliminated the two above possibilities, then this one can be checked by using a (good) infrared thermometer or (real) thermal camera to get an estimate of the temperature of the junction between the heat-sink and the IHS. If that reads back at close to 115 °C, then the package temperature sensor is bad (and something else is probably wrong with your CPU). If it reads back at close to the 66 °C being reported by the package temperature sensor, then either something is wrong with the core temperature sensor or the next (worst case) possibility is the case.
• Something is physically wrong with the thermal junction inside the package between the IHS and the CPU die. This is the absolute worst case scenario, as it means your chip is essentially useless (because you quite simply cannot cool it well enough for it to be practically usable. This is also astronomically unlikely (actually, it's beyond astronomically unlikely, it's even beyond the unlikelihood of a SHA-256 hash collision with two randomly chosen files), but it's still technically possible. There's unfortunately no practical way to check this one if you've eliminated all the other possibilities, because delidding the CPU to manually check will make it irrelevant (and also require use of a completely different cooling system).

CPU core temperatures of more than 110 degrees is too high and make the processor stop working. If really temp is over 110 degrees system will likely crash and there could be nasty situation. HWMonitor is showing incorrect values.

Go to your BIOS and check temperatures there, and if BIOS also says nothing this could be indicative that your Motherboard dosen't have any temperature sensors, thus explaining why HWMonitor is showing strange values.

If the temperature is high, then you can check the airflow, clean the dust in casing and components and check if the fan is moving properly. You can use Core Temp as the other answer suggested.

Your CPU temperature is reaching its very maximum. I think, any PC component having temperature over 100C is too much for extended period of time. It is recommended to keep it under 80C in the long run, 60-something is even better.

I always recommend to remove the original cooling fan of the CPU (which usually give you when you buy it) and buy a better cooler with bigger heatsink. I bought CoolerMaster HYPER TX3i, which is a cheap (under $30), but an effective one.

For my i3-9100F temperature with the original heatsink cooler: Idle - 65C, Load - 95 - 100C; after applying CoolerMaster: Idle - 30 - 42C, Load - 50 - 60C.

When a CPU reaches 100+ degrees, it should be restarted. If it still doesn't' resolve the issue, you might want to reset your PC or delete some apps. Another reason might be the heatsink or the cooler's problem. If you don't want to get new hardware, I recommend you turn the CPU voltage a bit lower. If I am correct, your CPU is not unlocked, so you can't really adjust your clock speed, but beware when turning your voltage down, turn it down bit by bit. If you notice instabilities, revert the changes.