those things are right. Have you ever heard about our lord and savior thermodynamics. A calorie is the amount of energy you need do heat up 1g of Water one degree Celcius. assuming your bodytemperature is 36°C and you drink 1L of 6°C cold water you burn 30Cal (or scientifically 30 kCal) If you drink around 3L of water per day this sums up to 100kCal added. And yes lying under AC burns calories. the higher the temperature gradient between body and the air outside the more heat the body loses. Therefore the body must burn more fat to keep up his temperature. But this effect is minuscule, if you really wanna burn calories by letting the heat flow outside, you should take a bath in cold water since liquids have a better thermal conductivity than air.  Fats will of course go batshit crazy about that and order a frozen sugary "coffee" with extra syrup and cookies. And since it is cold I burn energy.