But many people can't help think that it still makes sense in some way. Well, I'm going to explain to everyone why it doesn't work. Since I am not a physicist in any sense, the scientific details have been simplified. In a nutshell:
The problem in the logic lies with the laws of thermodynamics. The amount of heat lost by sweating and evaporation will never exceed the amount of heat gained by the hot drink you've consumed. Another problem is that the extra heat makes your blood vessels near the skin dilate to help cool your blood faster. The nerves in your skin can sense this, causing you to feel flushed and warm. Not exactly the result you are looking for.
The overall answer, is that hot tea will make you sweat more, and increase your cooling. But the amount of extra cooling won't be enough to offset the heating-up from the tea.