80-90C° is a high temperature. To make sure no damage is done to the CPU due to heat, let's try fix the problem.
Make sure that the CPU cooler is properly installed. The heatsink should be touching the CPU.
Have you applied new thermal paste? Coolers won't work that well without thermal paste.
Is the fan on the cooler spinning at a fast enough rate to cool the CPU down?
Do you have case fans to pull in cold air and push out hot air? Case airflow is key to good temperatures.
Feel free to comment any questions or concerns.
Hope this helped!
-Lachlan