Not really. ‘The University of Sydney's Ollie Jay, who researches how the human body responds to heat, says a hot drink can indeed trigger a net cooling effect through excess sweating.
But there is a crucial caveat: to produce that cooling effect, the sweat needs to be able to evaporate.’
Not sure if it's true - they say folks in hot countries eat spicy foods cos that makes them sweat & the sweating cools them down. (or it's to disguise the taste of unsavoury food!)
Anyway I'm all for a cuppa whether it's hot or cold outside.
Incidentally tea is supposed to have prophylactic properties which helped ward off disease when the early years of the industrial revolution led to extreme overcrowding in cities.
When I was in the Army, a cup of hot tea was usually waiting for us at the end of a route march in hot weather. And, yes, it did seem to help the cooling-down process, but I don't know why.