Last night was the first night whenre I didn't need to turn on my air conditioner.

Maybe "when" could also be replaced with "that," but I feel like the way I corrected things here is a more common way of phrasing things.

At the beginning of last night, I closed the window and the door of my bedroom, and then I turned on my air conditioner.

Alternatively, you could've just taken away the second comma, but I hope my corrections here also make things easy to read.

I turned off the air - -conditioner and opened my window and door.

The cool wind from outside immediately blew directly onto me.

You can take or leave the "from" I added to this sentence.

I slept naked without any covers, but I didn't feel either hot or cold.

It was the right temperature for people to sleep naked without any covers.

I especially checked the temperature on the weather forecast app on my phone last night, and it was 27 degrees Celsius.

I will remember it, as it's the nice temperature for people to sleep without any covers.

Before that, I was turneding on my air conditioner every night.

The original is also correct, but "was turning on ... every night" emphasises the repeated action a bit more I think, and so sounds a little more natural in this context.

After a while, my wife called me and told me that her bedroom felt really cool withould even though she didn't turning on her air conditioner.

"cool" for temperature has a little bit of a meaning of "cold, but not that cold", so it sounds a little weird when combined with strengthening words like "very"

Yes, it felt really coold.

She had just opened her window and door.

I could feel that the cool wind from the window blewwas blowing directly onto my body.

I turned off the air - conditioner and opened my window and door.

I slept naked without any covers, but I didn't feel either hot or cold.

"without a cover" or "without any covers" -> any is used with plural words, a for singular. Grammatically, either could work in that situation, but in terms of word choice, people tend to talk about covers more when talking about duvets and blankets.

It was the right temperature for people to sleep naked without any covers.

I especiallymade sure to checked the temperature on the weather forecast app on my phone last night and it was 27 degrees Celsius.

"especially" sounds a little unnatural here

I will remember it as it's thea nice temperature for people to sleep without any covers.