I have a sliding glass barn style door between a heated room, and a non-heated entrance. Here is a side view of said door :
The gap is 2-3 cm wide. How can I minimize that gap ?
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One thing you can do is to get some weather stripping and install it so that it just comes up to the glass slider. If the glass slider is one that free hangs without a track or guide at the bottom it will be somewhat problematic to have the weather stripping actually contact the glass as it will likely just push the bottom of the door way from the wall.
Here is one style that you would mount to the inside edge of the door opening behind the slider.
Will it look ugly? Probably - but then almost anything you use to try to seal up that opening will not be pretty. Comment: Using that type of door for an environmental barrier is anything but optimum.
It looks like the gap is caused by the hardware for this barn style door, which is a common scenario.
For the best seal, my recommendation would be some pieces of weatherstripping or gasket.
In the picture you show, you could place one piece vertically on the wall side of the door (on the end the picture was taken). If necessary, you could place another piece opposite that on the wall so when the door is slid shut they will 'mate' and make a seal.
When the door is open you may not even be able to tell that they're there - I can't quite tell from the picture.
Repeat a similar process for the rest of the door. Use two pieces placed opposite if one can't fill the gap.
Additionally remember that when possible, if one piece can create a seal, you'll likely want to place it on the wall so it will wear on the door- and not discolor the paint on your wall!
Your mileage will vary and I imagine part of your decision will involve the aesthetics of how the setup looks.