August rememberinds me of the good times when it was raining and I was going to school.

My dad puttingturned on the air-conditioning and the car feelinglt cold but in a good way.

AWe were accompanied by music on the radio and uswere occasionally talking about random things or life in general.

The Best summer monthMonth of Summer

August rememberinds me of the good times when it was raining and I was going to school.

MOr my dad puttingturning on the air-conditioning and the car feeling cold, but in a good way.

I would combine this with the previous sentence.

August reminds me of the good times when it was raining and I was going to school, or my dad turning on the air-conditioning and the car feeling cold, but in a good way.

Accompanied by music on the radio and us occasionally talking about random things or just life in general

Same issue as before. I would make this part of the previous sentence

August reminds me of the good times when it was raining and I was going to school, or my dad turning on the air-conditioning and the car feeling cold, but in a good way, accompanied by music on the radio and us occasionally talking about random things or just life in general.

You can choose to split it up another way, but your sentences were not complete sentences in the state they were in because you can not start a sentence with a conjunction (but, or, if, etc.)

BThe best summer month

Or you could say "the best month of summer"

August rememberinds me of the good times when it was raining and I was going to school.

My dad puttingIt makes me think about my dad turning on the air-conditioning and the car feeling cold but in a good way.

"It makes me think about" is another way to say "It reminds me of"

Accompanied by music on the radio and us occasionally talking about random things or life in general.

Just needed a period at the end of your sentence.