Sorry for double posting. I succesfully avoided washing the dishes, read through a few studies and I'm gonna answer a few of my own questions. I will not quote scientifically correct, pardon me, too tired for that.
Our body regulates its temperature through hydration. Body temperature will rise during excersise, hydration helps to balance it. A cold fluid indeed seems to do that more effectivly (why??) plus the normal increase of sweating after drinking is lower since we seem to physiologycally react to the fluids temperature as soon as we sense it. BUT the voluntary intake of cold fluid (speaking below 10°) is much lower. (1)There is no significant difference in the hydration status between the same amount of water of different temperatures.(2)
Still missing a few explanations and the stomache ache aspect. Also keep in mind that these are studies and studies can be wrong due to a bazillion external influences and tend to be rewritten every 5 years.
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Edit: AND you basically answered the rest of my quastions, thank you very much. So we're talking ice cubes to keep water cool and not to really ice it?