Every cpu cooler I've installed in the past 29 years has been designed to take cool air and blow it into the cpu Heatsink. NONE have ever sucked the hot air out of the heatsink.
I've only seen one variation to that theme...... a PC where there is NO fan on the heatsink at all and there is a scavenging system to exhaust the hot air from the heatsink, out the back of the PC.
Intel CPU's are known to run HOT, which also means they are drawing a lot of power. That's just one reason that I will never build a system with an Intel cpu. Since the 386 days, I've used nothing but AMD cpu's and never have I ever had an overheating problem.
One thing that will cause those Intel cpu's to overheat is Overclocking.
Without some kind of supercooler, overclocking an Intel cpu is just asking for trouble.
I'd check the bios to make sure that cpu is NOT being overclocked.
Also, remove the case from that computer for a while and see if that changes the cpu temperature. If it does, that means that the air flow through the case is insufficient.
Being an old tech (45 years now) I know very well that "Heat Kills" electronics.
Everything in my PC stays pretty much at room temperature, because I have 13 fans in my system to keep it cool.
My AMD 5200+ CPU is properly cooled by the stock AMD fan and heatsink. I can reach in and lay my finger on the cpu heatsink anytime and it's only slightly warm to the touch.
My first wife ran hotter than my cpu.
Good Luck,
Shadow