When sSummer aArrives

When the climate starts to feel a lot hotter and you feel the steam on the streets, that's when summer has arrived. I don't know how to describe it.

“When the climate starts to feel a lot hotter and you feel the steam on the streets,” is technically a sentence fragment. A lot of native speakers do this, but it's still good to complete the sentence.

The heat gets worse when the sun is in the center of the sky and. It feels like it's burns youing.

What you wrote is grammatically correct but it doesn't sound like what an English speaker would say.

Even with the fans, I still feel the heat.

When the climattemperature outside starts to feel a lot hotter and you feel the steam on the streets, I don't know how to describe it.

I think using "temperature" is better here because "climate" talks about the average temperature over many years. "Temperature" gives a more fluid and changing nuance.