Why does my car overheat when the ac is on during winter -26 deg celsius?

Have you considered not running your air conditioning in -26 degrees C weather?
I normally wait for it to get much warmer than that before using air conditioning.
I used to be a certified A/C tech. And I run my car's A/C at least once a week, 52 weeks a year. And there's a good reason for that, too. I'm sure you've experienced turning on A/C, any kind, only to have it blow out nothing but uncooled ambient car instead of blowing cold. 9 times of 10 it's because the refrigerant is too low. And the reason for THAT is, usually because nobody used the air for a long time.

You need to run your A/C regularly, once a week is not too often! And the owner's manual for my 2002 Toyota Camry even says as much: "Every week or two, run the A/C a minimum of 30 seconds." And they're right, regardless of ambient temperature, you still need to run the A/C anyway! Here's why: your A/C system runs off refrigerant, of course, but mixed into it from the factory, is several ounces of special compressor oil too. The purpose of that oil is mainly to lubricate internal seals, particularly the compressor seal, (the one right under the pulley). And that oil can only lubricate things if the A/C is running. That means, if you don't run your air conditioning, your compressor seal will dry out, because no oil got to that seal for several months. So that's the reason it is so common, for somebody to run the A/C after a long winter and find only warm air blowing out.

I run my air once a week no matter what the temperature is. During start and warm-up is the best time, since the car's cold anyway, and it only takes 30 seconds to a minute of operation for the refrigerant oil to circulate. Does it work? I can tell you, my 2002 Camry V6 is still on its original refrigerant 204,000 miles later.
 
OP car is not overheating.
And if the engine and the cabin are heat soaked, the AC compressor may actually engage. And since the evaporator gets warm, it’s probably enough to transfer some heat into the radiator and make OP temp gauge read a little higher than what he’s used to seeing.
 
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