Ok this is mostly guesswork here but..
A cup of drinkable tea is what? About 60 degrees Celsius? Compared to the human temperature of 38, it’s not a huge increase, and as a cup of liquid is really quite a small amount, there isn’t a huge amount of energy there.
Then you have the vasodilator effect, and the body’s sweating reaction.
Plus tea is still a liquid – it will hydrate you (so will beer, coffee, etc. etc.).
However, I’m pretty sure the human body can absorb colder drinks easier – which is why colder drinks are better for rehydration.
For keeping cool, it’s probably very close to six of one and half a dozen of the other.
Also,
I was always told that ice cold drinks, whilst drunk on hot days, cause the motabalism to go into a mini shock
This sounds vaguely familiar.
I always finish a shower on hot, on hot days, because it makes it seem cooler when you get out.
The body is very good at sensing difference in temperatures, but not much else. Therefore if you stick one hand into a bowl of ice water and another into a bowl of hot water, leave them to get accustomed, then stick them both in a bowl of room temp water, it will seem cold to the hot hand, and hot to the cold hand. That’s how I would explain what you have been feeling.