Well, I can sort of see the reasoning behind it. If you drink a cold beverage, you will expend calories heating it up. More calories burned = more heat. However, when you drink the hot tea, although you won’t expend calories to warm it up, the heat that’s in it WILL have to be transferred to you. So then logic says the ideal temperature to drink something in hot weather would be at body temperature. No calories burned heating it up, and it won’t have any extra heat that must be transferred to you.
However, on a more practical level, the amount of energy heating up a cold beverage is small compared to the amount of energy used to just sit around. A calorie is the amount of energy needed to heat 1 ml of wter 1 degree C. Let’s say you drink half a liter of cold water for lunch (let’s say it’s 10 degrees C.) So now we have 500 ml of water that needs to get raised 27 degrees (body temp is 37 C.) That equates to 13,500 calories. Seems like a lot at first…but a food Calorie (note the capitol C) is actually a kilocalorie, that’s 1000 calories. So you would burtn a whopping 13.5 Calories to heat up a cold beverage. Considering that manual labor burns 200-300 Calories an hour (from here, several types of labor there, I took the 200-300 range because it seemed on par with things like carpentry and moving heavy loads) we can see that the 13.5 burned from drinking the cold water is a pittance.
Given the immediate effect of a cooling sensation of drinking a cold beverage, over the immediate warming sensation of drinking a hot beverage, I’ll take the cold one and suffer those 13.5 Calories, especially since it’s spread out over the course of several minutes.