I’d say the answer is no, but if your cat is long-haired AND obese, then the answer is yes.
As long as you have air-conditioning or cross-ventilation and shade, your well-groomed cat should be fine.
A matted cat or a cat who is not regularly combed is a different story.
Mats turn a fur coat into a blanket. Dead fur that builds up over time, unless you comb it away, mixes with living fur. That makes the coat dense and heavy.
A bath will wash away excess oil that makes the fur stick together.
Go for a light, airy coat. If you accomplish that goal, then your cat can enjoy the warmth of summer. If you can’t keep the coat clean and combed, hire someone who can or get a lion-cut for your cat.