It's the fans. They are clogged with dust and other debris from the years of use. Notebooks are not air-tight and intake quite a bit of air over their lifetime (they need to push the air to the central components like the CPU/GPU to cool them). The units must be opened and cleaned periodically (depending on environment) to maintain peak operating performance. High fan speeds and poor thermal dissipation are signs that the fans aren't doing their job (they are likely clogged with dust and the exhaust is also likely blocked, preventing the output of the hot air blown off from the processing units). Computer fans work by pushing air taking from the environment onto the CPU/GPU. The hot air blown off the chips move through air vents in the back of the unit. Over time, dust settles on the fans, dropping their efficacy, and the vents, preventing the hot air from escaping. This bakes the components and results in the spike in over temperature.
Visit www.ifixit.com and pull up a guide on how to partially dismantle your notebook. If you are not technically proficient, bring it to a credible repair shop.
There are no "normal" operating temperatures for Apple notebooks, but there is an acceptable gradient. 82 degree Celsius is pushing the limits. The CPU's thermal threshold is 105 degrees Celsius (when that temperature is reached, the system will shutdown to prevent thermal damage).
And just an aside, regardless of locale, all temperatures should be reported as Celsius, never Fahrenheit when dealing with computer components. Official documentation always refers to Celsius.
This model of MacBook Pro has a totally passive heat sink, so the two temperatures you mention are on the main die / logic board and not some measure of how hot your heat sink itself is running. The only way to correct this difference would be to have a new logic board installed (or get a new CPU mounted on your logic board).
As a technician, I'm more worried when the heat sink isn't closer to ambient than to the core when stressing the CPU with constant computing load. Then, it might be worth it to crack the case and re-apply the thermal paste between the metal cover (the CPU heatsink) on the logic board and the finned device (a.k.a. the Mac heat sink part) that gets the heat from the CPU heatsink to the air flowing out the back hinge area of your Mac.
If you had a faulty CPU you should be able to expose that in a geek bench test where it would throttle itself down under premature overheating. If you still had warranty left, I would open a support ticket (visit a genius bar or call AppleCare) to document this. They can then enter your concerns and offer a logic board swap if you are out of spec. I've had good luck getting concerns on the record and having Apple cover a repair if they had the chance to cover it under warranty, chose not to, and then the device failed within a few months after warranty.
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Normal temperatures are around 30-50 C (86-122 F). Mine is around 30.6 C on low load and around 60-65C under very heavy load. It depends where you keep you mac, for example if you put it on bed sheets it can get very hot because the air flow is blocked :)