Isn't this fundamentally ridiculous? The expended energy from drinking a cold glass of water is so minute it is irrelevant. Instead of drinking warm water, you could put on a hat for ten minutes, or a jacket, or a heavier shirt; or move closer to the radiator for a few seconds; or eat something slightly warm; or walk around for a few seconds. It won’t matter. There are many, many more things that affect your body that make the temperature of a glass of water insignificant.
Basically. The fact of the matter is that the body is constantly producing more heat than it needs, and is expelling it. Mostly, to heat up the immediate environment (air, seat cushion, &c). Room temp is between 20-25C. Body temp is 37C.
When you drink cold water, some of the energy that was being wasted in one way will be temporarily diverted to heating the water to body temp. Your body doesn't have to burn 'extra' calories to do this.
Having said that: there are extreme situations where your body is in an environment that is either too hot or too cold for normal operations to mitigate. We can die of heat exhaustion/stroke or hypothermia. The case of the camper drinking icewater is an example of the latter: the body needs to go to extreme measures to adapt, and may fail. In which case, drinking hot or cold water can be critical.
But under normal circumstances, there is no 'energy' benefit to drinking warm water. Warm water is probably also at room temperature, say, 20C, which means the body is *still* warming it up to 37C. Water at body temperature would probably feel 'hot'.
Having said that, there is a noticeable effect from drinking hot/cold liquids when within the normal body temperature range. The reason is that the esophagus is close to the pulmonary vascular system, as well as the cardovascular system. Cold drinks can cool down blood passing nearby, and perhaps even pass to the brain through the carotids. This effect will 'trick' the body into thinking it is a different temperature, and provide some brief relief, while the body takes a moment to regulate temp according to surroundings.
The second discussion about digestion is also unrelistic, and much goofier. The body doesn't absorb water until it passes throuh the large intestine, which is to say: water absorption is the last thing the body does to a bolus before excretion. There is no delay in the stomach. Even if that was true, hesitation for thirty seconds can't have a noticeable effect on overall digestion.
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