How hot is your cup?

Here's the deal, after reading a bunch of blogs on the subject of coffees cooling I decided to do some tests by myself, and have thought up some of my own questions in regards to the subject.  The first question was about the difference that could be caused over the cooling period?  I already had a preference of letting my coffee cool to the point of being straight up cold.  So, with some research I also began to look at what chemical compounds in the coffees are changing over time in the coffee as it cools?.?.?.  This also led me to look at the fact that any solids in a brewed coffee will continue to extract until the temperature is diminished or until drink is finished, or all the coffee over-extracts.  Another thing that popped in my head was Newtons Law of Cooling, and how that could effect the temperature and overall extraction of a cup (which was touched on kinda @ jimseven.com) And finally 'shocking coffee', does it happen or exist?

So first thing is first, according to Newton's law of cooling, the rate of change of the temperature of an object is proportional to the difference between its initial temperature and the ambient temperature. An example from physics247.com about the law is as follows:

"Newton’s Law of cooling means that if a hot object is subjected to a very cold object, it will transfer its heat a lot faster than if the hot object that is subjected to a mildly cool object.

You are having dinner with your friend at a restaurant one evening. You place your order, and the waitress brings you your coffee much earlier than the rest of your meal. You want the coffee to stay hot until your food arrives so you can have them at the same time. You always add cream to your coffee, but know that from Newton’s Law of Cooling that a hot object transfers heat to its surroundings at a rate proportional to the difference in temperature between the two. So your choice is to either add the cream to your coffee now, or add the cream to your coffee once your meal arrives. You think about the problem for a moment and come to a conclusion.

If you add the cream right away the temperature difference between the coffee and its surrounding air is brought closer together than between just the hot coffee without cream and restaurant air. A hot object cools at a rate that is faster when the difference between the temperatures of liquid and the surrounding air and cup is the greatest. Adding cool cream at the beginning slows down the cooling speed because it decreases the difference in temperature between the hot coffee and its surroundings. If you did not add cream right away the difference in temperatures of the hot coffee and restaurant air and cup is the greatest, so it would cool more rapidly and then when the cream would be added, it would cool even further. You add your cream to your coffee as soon you got it,and enjoy a nice hot cup of coffee when your meal arrives all thanks to Newton’s Law of Cooling to help you out."

Okay, with that example aside noting that no one should put cream in their coffee for any reason, how does this apply to the discussion of cooling coffee and flavor?  Well, this whole idea got me thinking about how cup temperature plays into how we perceive the flavors in the coffee we are tasting.  The quick experiment that I have done a few times now was to get a preheated cup and put a designated amount of coffee (2.5oz in this case) into the cup, as well as getting a room temperature cup (69 degrees all times I have done this experiment) with the same amount of coffee in it and log experience over the period of time until they both reach room temperature.  The first thing I really noticed was that the cold cup (this is my opinion) tasted better than the preheated cup every time we tried this and most people who tried it too agreed.  The hot cup on the other hand seemed to lack a lot of flavor up front.  Is it possible that the cooler cup lowers the temperature enough in the coffee (via Newtons law of cooling) to "stabilize" the chemical changes that would normally occur over the period in a preheated cups cooling? 

My other question is that with so many volatile chemicals in coffee that rapidly change, and continuous extraction occurring throughout a coffees lifespan after brew time to finish, is it possible that a cold cup slows or stops some extraction from taking place and almost suspending the coffee in time in accordance with Newtons law of cooling? And additionally that the preheated cup contributing to more extraction occurring as well as more chemical development in the coffees life? 

All of this led me to try some shots of espresso with room temperature cups and preheated cups.  Between a group of six people, we split shots from the Synesso of a S.O. Guatemala Ayarza and noticed a huge difference between the shots.  First off we noticed that again the 'hot' cup's shot was really hard to taste in comparison with the colder shot, where we found lots of immediate descriptors.  This could just have been our group but we all seemed to tend towards the cooler shot throughout the whole cooling process as well as when the shots both made it completely to room temperature.  

I am really not sure where this leads me ultimately in the grand spectrum of coffee, but I find myself questioning the intuition of pre-warming cups, and what I find to be desirable.  It also makes me question customers perceptions of what good is? If I a "professional" coffee person is constantly questioning and redefining my methods of delivering what I feel to be the best representation of what coffee should be, than how should I approach it?  Another thing is the aspect of maybe it is just a case by case coffee conundrum that should be addressed in the moment.  Too romantic? I don't know.  I have spent the past few days thinking about the thermodynamics of coffee and the heat loss vs. chemical changes vs. time, and how my perception fares against the other 6.5 billion people in the world.  

One of the things towards the end of my list on the thoughts of cooling coffee was influenced by Ted R. Lingle's book: "The Basics of Brewing Coffee" where on page 20 in table 7 (in my book) he has a list of chemical changes resulting from variations in temperature.  What I take away from it is that all of the taste-contributing compounds are effected by water temperature (no big surprise) at time of extraction.  But if the extraction is ongoing then wouldn't it make sense that the compounds are also constantly changing in the coffee with varying amounts and attributing to bad flavors?  Is this what makes coffee so dynamic over time or is it potentially negative?

As a final thought about the pre-heated cup vs. the cold cup, I think that maybe the added heat from the hot cup is essentially causing some continued extraction.  Higher heat = more extraction.  So although the heat loss should be more rapid in the hot cup over time (via NLoC) the cooler cup lowers the immediate temperature and slows extraction and chemical changes. I don't know really, I wonder what the truth is?