ali.khal1l3579,
On behalf of Tom's Moderator Team, welcome aboard!
47°C is very high for idle, and 90+°C is too hot, regardless of the type of workload.
Here's the nominal operating range for Core temperature:
Core temperatures above 85°C are not recommended.
Core temperatures below 80°C are ideal.
Core temperatures increase and decrease with ambient temperature. What is your ambient (room) temperature? Standard or "normal" is 22°C or 72°F.
There are several different "stock" Intel coolers. The stock cooler for the 77 Watt 3570K is a 95 Watt TDP (Thermal Design Power) cooler:
Intel® Core™ i5-3570K Processor -
https://ark.intel.com/products/65520/Intel-Core-i5-3570K-Processor-6M-Cache-up-to-3_80-GHz
The same cooler is also used on the 3770K. It's easy to identify by the copper core in the center of the aluminum fins, which is visible from the bottom. If your stock cooler doesn't have a copper core, and is instead all aluminum, then it's probably a 65 Watt TDP cooler from an i3 or Pentium, which is not adequate for your 3570K.
However, it's highly likely that your stock cooler has popped a push-pin loose from the motherboard, which is a very common problem. This causes poor contact pressure between the cooler and the CPU, resulting in high temperatures in BIOS, as well as in Windows at idle, and especially at 100% workload.
You can troubleshoot this problem by pushing firmly on each corner of the cooler for about 30 seconds while watching your load temperatures. When you see a significant drop, you've found the loose push-pin.
The push-pins can be deceivingly tricky to get them fully inserted through the motherboard and properly latched.
(1) To re-seat a single loose push-pin, rotate the latch mechanism in the direction of the arrow counterclockwise 90° then retract the pin by pulling upward. Rotate the latch clockwise 90° to reset the pin, but do NOT push on the latch yet.
(2) To get the pin fully inserted through the motherboard, push only on the leg, NOT on the top of the latch.
(3) While holding the leg firmly against the motherboard with one hand, you can now push on the top of the latch with your other hand until the latch clicks.
(4) If you're re-seating the entire cooler, then be sure to latch the pins across from one another, rather than next to one another. Use an "X" pattern, so as to apply even pressure during installation.
Intel Stock Cooler Installation -
https://www.youtube.com/watch?v=5qczGR4KMnY
If you don't intend to overclock and your ambient temperature isn't too high, then the stock cooler should be adequate.
Once again, welcome aboard!
CT