The current evolution narrative is this: (IANAEB)
human evolution began with the descent from the trees to the nearby plains - occasionally at first, then more and more as the dominant environment.
With the move to the plains came bipedal movement - mostly walking on two feet.
Proto-humans supplemented their gathering with scavenging from kills left from other predators, protein being a good source of nutrients.
Somewhere along the way humans figured out thatit was just as handy to kill their own food as to wait for the bigger animals to leave their kills
Somewhere there too, they figured out tools to chase off hyenas or other pesky critters - pointy sticks, clubs, fire.
The standard human hunting method tended to be chasing down four-legged animals. Humans on two feet were incredibly better endurance runners than most four-legged animals, and could chase them to exhaustion… then use their tools to kill them.
Somewhere in there they discovered fire was easy for softening up raw meat so it was (like the carcasses they used to pick over) softened up.
The key is the long-distance running. generally clothing was unnecessary on the plains of Africa, but the human sweat system is remarkably well designed for shedding all the heat generated by distance running, even in the hot sun. The reason why we have so litle hair, except where it protects from heat stroke or chafing, is so the sweat glands can work during nude marathons.
Clothing is an afterthought that, I assume, originally started as blankets that helped against cold nights on the savanah and later allowed us to move into colder climates.
So the OP has cause and effect backwards. We had no hair and developed clothes as a solution for colder situations.
Similarly, we probably lost our tolerance for extremely unhealthy (rotten) food because we had fire to help purify food. Even rotten meat, if cooked, is not full of dangerous live bacteria. Spices dull the bad taste.