Cpu running at 76- 90 at idle how long can i let it run like this.

My cpu cooler which is a stock intel cooler works however the little latches that lock it into place on my motherboard have broken over the years and its time for a new one. It is still installed but because of the latches it is unable to cool my pc properly. I will order a new one from Amazon and it will be delivered in 2 days. However if I was to keep using my pc during that time. would it fry my cpu? it currently runs between 76- 90 celcius.

The motherboard should turn the pc off if it gets to a temp that it deems too high for safe operation :)

The CPU will throttle itself if it gets too hot (unless you disabled that option in BIOS like many overclockers do). If the CPU reaches a critical temperature it will shut itself off and tell the motherboard to cut power to everything else.

Personally I would not dally replacing the cooler if it idles that high. It will degrade your cpu. If it is idling that high then it must be over 100 if you do anything with it and it must be performing poorly because of the throttling. The throttling doesn't make it "safe", it is not meant to be run that way for long.