No. You can be completely exerted without sweating or completely soaked in sweat without feeling exerted at all. I’ve experienced both and when I’m in better shape I will sweat more without feeling exerted, while when out of shape I can feel exerted without being sweaty. The amount of energy required to move your body is about the same whether you are fit or not. So the heat production and therefore the sweat production would be the same. Being in better shape makes the body better at producing sweat to cool you down. So more sweat and less exertion.
How fit you are doesn’t determine how much you sweat. Becoming more fit can make some people even sweat more.
Being physically fit causes tasks to be less exerting which can reduce sweat.
No. You can be completely exerted without sweating or completely soaked in sweat without feeling exerted at all. I’ve experienced both and when I’m in better shape I will sweat more without feeling exerted, while when out of shape I can feel exerted without being sweaty. The amount of energy required to move your body is about the same whether you are fit or not. So the heat production and therefore the sweat production would be the same. Being in better shape makes the body better at producing sweat to cool you down. So more sweat and less exertion.