After some time, I would like to summarize, what was is actually done and bring some info.

I was struggling with some not working parts like EEPROM, correct temperature measuring, heating... , but finally I have found the root cause and fixed it. Last part, which needs to be clarified, was user interface. I have made some, how to say "preliminary" version, but It looks fine from my side. Maybe I will modified it a little bit afterwards.

What is actually working/done:
 - User interface
 - buttons handling (rotary encoder, user buttons)
 - temperature measuring (ambient, heating)
 - display controlling (SSD1306)
 - parameters saving (EEPROM)
 - calibration (external more precision temperature meter required)

What needs to be fixed/done:
 - sleep mode
 - protection handling
 - power bar handling
 - pen detection
 - stand detection
 - °C/F switching
 - brightness regulation

Here are some videos, how the real prototype looks like.

Cold heating from ambient to target temperature (25->200)

User interface, menu handling

Actually there is still lot of work. Next step is to verify, if heating algorithm is the correct one, or some tuning is required.