Nah.
Just like people need different amount of sleep, people produce different amounts of sweat at a comparable level of effort.
My body has settled on an almost Pavlovian response.
A simplified protocol.
Pulse up = sweat on.
It doesn't bother waiting for any core temperature increase.
Only times I can get a decent pulse increase w/o sweating is when I'm simultaneously at risk of hypothermia.
And yes, I know this by trial and measurement.
Literally within seconds of stopping, I start shivering.

I experienced considerable amounts of misery all those years I believed the "you're simply not dressed right" - crowd.

On contrast, dear Mum has always found it difficult to exercise during Summer. She's a very marginal sweater, and prone to overheating.
My brother is somewhere inbetween.