How to find what is making the Mac run hotter and causing the fans to run more often

If you don't need to use the MBP screen while using the external monitor you can disable it using a small magnet.

A small magnet placed on the left side of the MBP keyboard, more or less above where the SD card reader is placed, will make it think that the lid is closed. The GPU will need to do less work to drive just one screen (the external) and use less power, and with the lid still open the airflow will be beter.

I use this on a 2011 MBP, other versions may need to have the magnet placed at different places for it to detect a closed lid. And if you try this, please use the smallest magnet available.

I understand your concerns (justified or not), you love your Mac and want to keep it alive as long as possible.

Here are some home remedy (Do it Yourself)-- (also available where you live).

If you want to keep your Mac cooler during HOT games, go to pharmacy and buy what they call a gel-pack (gel balení). Freeze it!

Then put it under your Mac with a towel in between (to prevent freezing).

That will provide additional cooling for few hours. Have second gel-pack if you want to continue gaming for 24 hours a day :)

As for your temperature reports, so far they look normal based on this example.

Throttling

This test wouldn't be complete if we didn't address the subject of throttling. Prime 95 and Furmark can extract the maximum performance out of the hardware. When both programs are run simultaneously, the core frequency drops (caused by Prime 95) to 1.2 Ghz. Running Prime 95 alone, we measured temperatures between 92 and 104 degrees Celsius (197.6 and 219.2 degrees Fahrenheit), and the word "Throttling" flashes repeatedly in HWiNFO. Furmark on its own cycles through all available Turbo Boost steps. After about one hour, the temperature settled at a fairly consistent 85 degrees Celsius (185 degrees Fahrenheit) with the fan system running. We never measured above 100 degrees Celsius (212 degrees Fahrenheit) with Furmark. This limitation might be due to the power adapter: in the above scenario, the system would require 86.6 watts - but the power adapter can only supply a maximum of 85 watts. Immediately after running our different tests, we subjected the system to 3DMark 06 and CineBench R11.5. The results were identical to after a cold boot.

The fastest way to quick check is to use the surface temperatures as shown here.