Hot Drinks Cool You Down Myth

People take their tea many different ways, my usual method is to make it and set it down to let it cool slightly before forgetting i have a cup of tea and having to make another one but as we are in the season of Sun, Sea and people annoyingly asking 'Hot enough for ya'?, a persistent myth is that drinking a hot drink in these high temperatures can actually cool you down.
It's always seemed a bit weird to me and a few years ago i went and asked people from hot climates if they drank hot drinks back home to cool down and a hot and sweaty Indian said they tended to drink cola when it gets hot, a Greek looked at me as if i was mad and said if you they the choice between a cold drink and a hot cup of tea in 40c Greek summer heat, there is no doubt which he'd choose and it wasn't the tea.
The Chinese person said that where the summers in Hong Kong were stiflingly hot and they do drink tea in Summer but its served cold but the Thai cleaning lady threw me back into confusion by saying sweet, hot tea is exactly the thing they drink over there to cool themselves down in the heat which my much travelled neighbour agree with followed by a lengthy conversation about tea drinking in Bangkok and how drinking iced drinks didn't agree with his stomach and he had to use the toilet frequently afterwards.
I did find a couple of scientific types who explained that the assumption is that by drinking something hot, you bodies core temperature increases so you sweat and sweating cools you down but as the sweating only cools you down to the temperature you were before drinking the tea elevated your temperature in the first place, it's quite pointless and if someone hands you a hot cup of tea when you're hot, you would be better off waiting for it to cool down and pouring it over yourself.
So with a highest level heat warning in place for early next week should we be putting the kettle on or throwing out the vegetables from the freezer and filling it instead with ice cubes and the result is overwhelmingly bin the Broccoli, unplug the kettle and only offer my neighbour a cold drink if a toilet is close.