The processor is fanless from the beginning
The i7-2600 is an LGA1155 "desktop" processor with a nominal TDP rating of 95W, so it deserves a decent heatsink AND working fan. If the processor is "fanless from the beginning" (whatever that means) I'm not surprised it's getting hot with intensive workloads.
Check the fan on the CPU heatsink. If it's an air cooler, make sure the fan is spinning
all the time. If your CPU is cooled by an AIO, make sure the pump motor is working and the radiator fans are spinning.
At night the computer works very well
But during the day the program seems to freeze
Same room temperature
You must be doing something different during the day. If the room temperature remains constant, day or night, you can factor that out of the equation. Are you running more intensive tasks during the day?
It is possible that the possibility is from the power supply
No. A PSU doesn't cause high temperatures (apart from any wild heat emitted into the computer case). The CPU only draws as much power as it needs at any moment in time from the PSU. If the CPU is idling, it will generate very little heat. If the CPU is running at 90%, it will generate approximately 85W (90% of 95W). This needs to be dissipated by the cooler.
If you can remember back to the days of old fashioned Tungsten filament electric light bulbs, you wouldn't touch a 100W light bulb (close enough to the 95W dissipated by the i7-2600 at 100% load). It would burn your fingers.
The i7-2700 dissipates a similar amount of power under a heatsink/AIO block and needs to be cooled properly. If the CPU fan is not spinning, the i7-2600 could get rather hot (obviously).
The CPU will not feel as hot as the surface of a 100W bulb because it's covered by a heatsink. Nonetheless, the Silicon die inside the CPU will head up towards 100C (212F) when stressed.
If the fan isn't spinning, fix it.