Sucks for the landlord's power bill, but the people who commented here can do better. Sorry to lump you in with them. I wouldn't want a landlord micromanaging my window use by shutting it themselves and demanding I keep it shut, especially if I had some valid reasons.

I suggested a dehumidifier because damage/mold was brought up, definitely wouldn't be very viable as you suggest (especially in regards to temperature). Thanks for keeping it grounded and fair, and you are right that hot air would be pulled in, but I'm not too sure about that having a major effect to the point of very expensive damage or major effects on power, especially if OP's door is shut and considering other factors, such as climate, room size, and it being a single window.

Some of the arguments here in the larger thread do make sense, pulling in hot air and another commenter suggesting that it would cause an effect across the house, pulling outside air from other cracks and openings and increasing humidity/temp throughout the building, but I feel that the effect on the house/system is minimal if it's a single window in a small room.

I have a weather app (Breezy Weather) that shows me a humidity graph, that could be helpful for OP if they are reading this.

So, now the argument is shifting, we care about the landlord's power bill. We care about the landlord's rights, we care about the landlord's property like it's our job (worrying about potential, speculative damage), but the second it comes time to care for OP in a thread where they are seeking support? That doesn't seem to be what happened, based on the responses here.

A/Cs do take care of humidity, I doubt very expensive damage could be caused from a small, closet-sized room from a single window - especially if OP closed the window for periods of high humidity conditions.. OP could agree to be held responsible for damage, they might have already done so in their rental agreement/etc.

Let me put OP and their landlord on separate sides of a scale, do I care more about the person struggling who just wants to keep their window open for fresh air (and a number of other valid reasons) or the person who could easily just tolerate a tenant having a single window being open in a small room for most of the day in California? The answer is easily the person in distress, who should be able to own and afford their own home and live a dignified life.

You said it yourself, you sympathize with OP. Feeling bad for them isn't the same as caring for them and understanding that they experienced trauma from their landlord's actions. The people in this thread added to that trauma.