"Cold" is an adverb meaning "completely" here. It's a word describing HOW she passed out. It is not being used to describe temperature. "Hot" cannot be used here because it is never used as an adverb.

she passed out and she passed out cold are both correct she passed out cold is just emphasizing the sentence.

correct→: why is the word "cold" used here

She passed out “cold” implies that it was sudden and/or completely. She passed out means that she was first light headed or wobbly and maybe even first sat down before she became unconscious. She passed out cold implied that one moment she was fine and the next moment she was unconscious. “Cold” can be used in ways that do not refer to temperature: He gave them the cold shoulder. He was cold to them. He was trying to make a sale and started making cold calls. He stepped up to make his speech and realized he was in a cold (unfriendly) room.

You can say: She passed out. She is out. (Could have different meanings. One of them is 'not conscious'. She is out cold. (not 'passed out cold'. This is just a stronger way to say 'She is out' and doesn't have the other meanings that 'she is out' does. )