I can answer the second part of your question. Hot beverages will cool you down more than an equal amount of cold beverage in a hot dry environment such as s desert.

The reason is that drinks are ingested internally and enter the gastrointestinal tract, where they raise the core body temperature. We are FAR more sensitive to changes in core temperature than to surface temperature, and the body responds by increased sweating. In a hot, dry environment sweat quickly evaporates and cools you down.

This cooling effect is much stronger than the heat added by the hot tea. This is because while a gram of hot tea that is 50 degrees hotter than body temperature will only add 50 calories of heat to the body, a gram of sweat evaporating off your skin will take away 586 calories of heat from your body. This is because of the high latent heat of vaporization of water.

The same mechanism also works with spicy foods. Capsaicin directly stimulates the heat receptor, causing people to sweat, which cools them down. This is one reason why tea and spices are so popular in hot climates like India.