Every morning, I brew my coffee in a French press or a Chemex pour-over glass coffee maker. In general, my first cup tastes good, but the second cup tastes burned after I reheat it in the microwave or on the stove.
My question: is there a way to heat up coffee and have a cup of coffee that is as close to the first cup as possible?
Here is my current reheating process: I usually microwave the second cup for two minutes in a new, clean cup, or reheat it on the stove.
My first read of your title was literal, and I thought, "Sure, you can probably reheat coffee and make it taste like dirty porcelain." :-)
A number of things can change the taste. Just sitting out, volatile components that contribute to the aroma evaporate. Any form of heating speeds that up. Aroma contributes a lot to the taste. So this affects the flavor profile, generally in the direction of less-tasty, and with much less of the familiar coffee aroma.
But you also get some evaporation of the water, which makes the less-tasty coffee a little more concentrated, so that much more noticeable. Again, there's some evaporation just sitting out, and heating speeds it up.
If you overheat it to near boiling, either the whole cup in a microwave and then let it cool to drinking temperature, or heat it on a stove and the bottom is what gets very hot, you can scorch it and produce off flavors. I'm not sure if the jury is in on whether heat near boiling also breaks down some of the flavor compounds in the extracted coffee, which would affect the taste.
If you need to reheat, avoid doing it on the stove. If you do it in a microwave, don't heat it more than necessary (two minutes is a lot of time for one cup of liquid unless you have a low-power microwave; better to do it in shorter increments and check it to avoid overheating).
The best solution is to get a good thermos and keep the hot coffee in that. You may not need to reheat it. But if you do, you will likely need to raise the temperature only a small amount. Whether that tastes like the first cup will depend on how discerning your palate is, but it will be a lot closer to the taste of the first cup.
Alternative
Another approach requires a little more time, but it gets you a "first cup" every time. That is to brew one cup's worth at a time. With pour-over, that would add a lot of time (OTOH, it might serve as a good excuse to procrastinate something). If you use a small French press or just put in one serving worth of coffee and water, it would add only rinsing time and heating some water after the first brew in terms of work.
An Aeropress is designed as a single-serving brewer. You can use it like a French press or brew a serving quickly, and it can be rinsed out quickly.
As a time saver, if you consume the second cup within the same eight-hour workday as the first cup, most people wouldn't taste the difference if the coffee for both servings is ground at one time and what's needed for the second serving is kept in a small air-tight container until use.
