Again... you really can't use core temps to justify anything.
If you install the program realtemp, it should give you cooler readings. The reason behind that is because those program depend on a tjmax. The tjmax on CoreTemp is 100C. Realtemp is set default of 95C, which in turn diplays the temp 5C cooler.
By using a program that shows the Tcase reading, would be the same sensor your Bios uses in the health monitor. This would also apply to the MB's chipset utility app that diplays the CPU temp as a single reading. Its better to go by that to figure out if your HS is on properly.
Typically in an abient room of 78-82F, the Tcase should be around 30-35C. If its above that, it may indicate airflow problem. If the Tcase is sitting in the upper 50's, then I'd say its a HSF problem.