I read somewhere that too cold water is what gives coffee its acidity, how does that take place?
Furthermore, does that apply only to the water during the brewing process or as my cup of coffee cools down, the acidity increase?
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That's correct: as your cup cools, perceived acidity increases. This is due to variation in the chemical species affected by temperature.
Coffee is like ice cream. Ice cream is least sweet when it's stone cold, and tart and heavy when it has melted. Similarly, coffee is sweetest (and best) while it's hot, and is bitter or acrid when it has cooled. Furthermore, the cooler temp has led to chemical degradation and thus the awful taste. However, you won't perceive its flavors when the coffee is too hot -- so let it cool a bit.
As for your question whether the on-contact brew temperature affects end-result sweetness-sourness: there are a lot of baristas and coffee R&D pros who do temperature-control brewing, especially for espresso, in order to modify the flavor of the coffee.
I believe that varying temperature affects coffee flavor in a gradient.
For cold brew (in case you're also curious about that), the cold temperature is a different environment entirely. Coffee is just as soluble, however less energetically kinetic, so more time is substituted for the lack of temperature. The end result is a brew product that functions naturally as a cold product -- nice, sweet, characteristic.
As far as I see, there are a few questions mixed here. Let me clarify this.
Many different acids are there in your cup: Malic, tannic acid, maleic, oleic, oxalic, caffeic, chlorogenic acids, etc. Also, the carbon dioxide that's produced when the organic molecules are reduced during roasting have an effect on acidity when it's solved in your final cup. All these acidic components are responsible for the overall acidity of the final cup. However, during roasting, generally, the large organic acidic compounds are reduced and overall acidity decreases.
I hope this paragraph answer the main question and @glls's remark. For the second question, I have probably noted a very nice resource below, but my institution does not have access to that paper. If someone could help, we can learn more.
O. Fond, “Effect of water and coffee acidity on extraction dynamics of coffee bed compaction in espresso type extraction”, In: Proceedings of the 16th International Scientific Colloquium on Coffee, ASIC (Kyoto). (ASIC, Paris, 1995) pp. 413–420.
The acidity of the coffee depends on the variety/origin of the coffee (mostly) and the grade of roasting. The more you roast your coffee, the less acidic it becomes.