Ah. I see what you’re saying. You’re saying the heat from the hot water compensates for the increase in sweating.

I suppose it’s worthwhile investigating the relationship between the energy in the water and the energy lost through sweating. And indeed some people have studied that:

“Yes, the hot drink is hotter than your body temperature, so you are adding heat to the body, but the amount that you increase your sweating by—if that can all evaporate—more than compensates for the the added heat to the body from the fluid.”

https://www.smithsonianmag.com/science-nature/a-hot-drink-on-a-hot-day-can-cool-you-down-1338875/