An easy way to see if it's an incorrect sensor is to point a house fan at the case with the side off. Turn it to med or so and it should drop the temps quickly. If it doesn't, you have a bad sensor. If it does, you have a bad cooler.
It's been a long time since I used the stock Intel fan. Last time was on my E6600. It was a mess. And the clips can break. Though it would wiggle bad so you'd notice that. Are you using a stock fan, or the stock fan that came with that CPU? The 4590 should have a copper slug in the center of the heatsink. Lower end models were just aluminum. I would argue if you are having a temp issues I'd just upgrade the cooling. Aftermarket coolers cool better and are quieter. They aren't that costly either. One of these might be worth it.
I tried your house fan strategy and the temperature did not drop (even with the fan on pull power) but my computer still makes a buzzing noise that signifies that the cpu is too hot so clearly it was overheating, my conclusion is that the paste just needs replacing.
I've been testing to see if a house fan would help lower the temperature of my CPU by holding it towards my pc with the case open, the temperature did not move from 100C and my computer continued to buzz, which means it was still extremely hot. So from this I assume its the paste that's causing the problem, not the misplacement of the fan, would I be correct?
I rotated the fan as I thought maybe I put it on the wrong way and it seems to have improved the temperature control.
It now idles 40-50C instead of the 50-65C, AND the CPU no longer shoots straight up to 100C, but instead slowly crawls up (takes like 20-30 seconds), which is still not too good, so I'm hoping new paste will resolve the issue now.
this might be a silly question , but if its a stock cooler/fan,, did you wipe of the "thermal paste" from the heatsink part? if so did you apply paste. if not, you will be hitting high temps. and getting crashes/shut downs.